Properties

Label 94050bp
Number of curves $8$
Conductor $94050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bp1")
 
E.isogeny_class()
 

Elliptic curves in class 94050bp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
94050.cf7 94050bp1 \([1, -1, 0, -19464192, -29001622784]\) \(71595431380957421881/9522562500000000\) \(108467938476562500000000\) \([2]\) \(12386304\) \(3.1478\) \(\Gamma_0(N)\)-optimal
94050.cf5 94050bp2 \([1, -1, 0, -300714192, -2007032872784]\) \(264020672568758737421881/5803468580250000\) \(66105134296910156250000\) \([2, 2]\) \(24772608\) \(3.4944\)  
94050.cf4 94050bp3 \([1, -1, 0, -392823567, 2993013455341]\) \(588530213343917460371881/861551575695360000\) \(9813610916904960000000000\) \([2]\) \(37158912\) \(3.6971\)  
94050.cf6 94050bp4 \([1, -1, 0, -290026692, -2156305185284]\) \(-236859095231405581781881/39282983014374049500\) \(-447457728398104407585937500\) \([2]\) \(49545216\) \(3.8410\)  
94050.cf2 94050bp5 \([1, -1, 0, -4811401692, -128455135560284]\) \(1081411559614045490773061881/522522049500\) \(5951852720085937500\) \([2]\) \(49545216\) \(3.8410\)  
94050.cf3 94050bp6 \([1, -1, 0, -508023567, 1094171855341]\) \(1272998045160051207059881/691293848290254950400\) \(7874268990681185294400000000\) \([2, 2]\) \(74317824\) \(4.0437\)  
94050.cf8 94050bp7 \([1, -1, 0, 1961216433, 8608069175341]\) \(73240740785321709623685719/45195275784938365817280\) \(-514802438237813573137455000000\) \([2]\) \(148635648\) \(4.3903\)  
94050.cf1 94050bp8 \([1, -1, 0, -4820463567, -127946970264659]\) \(1087533321226184807035053481/8484255812957933638080\) \(96640976369473962846255000000\) \([2]\) \(148635648\) \(4.3903\)  

Rank

sage: E.rank()
 

The elliptic curves in class 94050bp have rank \(0\).

Complex multiplication

The elliptic curves in class 94050bp do not have complex multiplication.

Modular form 94050.2.a.bp

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} + 4 q^{7} - q^{8} + q^{11} - 2 q^{13} - 4 q^{14} + q^{16} + 6 q^{17} + q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.