Properties

Label 95370.j
Number of curves $8$
Conductor $95370$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 95370.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95370.j1 95370c8 \([1, 1, 0, -58157343448, -5398298602443968]\) \(901247067798311192691198986281/552431869440\) \(13334362366406991360\) \([2]\) \(191102976\) \(4.3774\)  
95370.j2 95370c7 \([1, 1, 0, -3659249368, -83158963742912]\) \(224494757451893010998773801/6152490825146276160000\) \(148506171813835175905055040000\) \([2]\) \(191102976\) \(4.3774\)  
95370.j3 95370c6 \([1, 1, 0, -3634834648, -84349518266048]\) \(220031146443748723000125481/172266701724057600\) \(4158099399266859279974400\) \([2, 2]\) \(95551488\) \(4.0308\)  
95370.j4 95370c5 \([1, 1, 0, -718138273, -7402169105123]\) \(1696892787277117093383481/1440538624914939000\) \(34771100456049459243291000\) \([2]\) \(63700992\) \(3.8281\)  
95370.j5 95370c4 \([1, 1, 0, -470314993, 3883691455213]\) \(476646772170172569823801/5862293314453125000\) \(141501509375851001953125000\) \([2]\) \(63700992\) \(3.8281\)  
95370.j6 95370c3 \([1, 1, 0, -225651928, -1336600870592]\) \(-52643812360427830814761/1504091705903677440\) \(-36305117333577721561743360\) \([2]\) \(47775744\) \(3.6842\)  
95370.j7 95370c2 \([1, 1, 0, -54883273, -60334208123]\) \(757443433548897303481/373234243041000000\) \(9008967294564907329000000\) \([2, 2]\) \(31850496\) \(3.4815\)  
95370.j8 95370c1 \([1, 1, 0, 12534647, -7222370747]\) \(9023321954633914439/6156756739584000\) \(-148609140617923831296000\) \([2]\) \(15925248\) \(3.1349\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 95370.j have rank \(1\).

Complex multiplication

The elliptic curves in class 95370.j do not have complex multiplication.

Modular form 95370.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} + 4 q^{7} - q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + 2 q^{13} - 4 q^{14} + q^{15} + q^{16} - q^{18} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 3 & 12 & 4 & 6 & 12 \\ 4 & 1 & 2 & 12 & 3 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 3 & 12 & 6 & 1 & 4 & 12 & 2 & 4 \\ 12 & 3 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.