Properties

Label 377377j
Number of curves $4$
Conductor $377377$
CM no
Rank $0$
Graph

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

Elliptic curves in class 377377j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
377377.j4 377377j1 \([1, -1, 0, 98749, 13588680]\) \(22062729659823/29354283343\) \(-141687519028542487\) \([2]\) \(2580480\) \(1.9769\) \(\Gamma_0(N)\)-optimal
377377.j3 377377j2 \([1, -1, 0, -611896, 133403427]\) \(5249244962308257/1448621666569\) \(6992220097790248321\) \([2, 2]\) \(5160960\) \(2.3234\)  
377377.j1 377377j3 \([1, -1, 0, -9017111, 10423067630]\) \(16798320881842096017/2132227789307\) \(10291856283477131363\) \([2]\) \(10321920\) \(2.6700\)  
377377.j2 377377j4 \([1, -1, 0, -3577001, -2496644708]\) \(1048626554636928177/48569076788309\) \(234433656963500975981\) \([2]\) \(10321920\) \(2.6700\)  

Rank

sage: E.rank()
 

The elliptic curves in class 377377j have rank \(0\).

Complex multiplication

The elliptic curves in class 377377j do not have complex multiplication.

Modular form 377377.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + 2q^{5} + q^{7} - 3q^{8} - 3q^{9} + 2q^{10} + q^{11} + q^{14} - q^{16} - 2q^{17} - 3q^{18} + 8q^{19} + O(q^{20})\)  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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.