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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 23520bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 23520.m3 | 23520bf1 | \([0, -1, 0, -312558766, 2126996800216]\) | \(448487713888272974160064/91549016015625\) | \(689321611854225000000\) | \([2, 2]\) | \(5160960\) | \(3.3864\) | \(\Gamma_0(N)\)-optimal |
| 23520.m4 | 23520bf2 | \([0, -1, 0, -311487136, 2142304820440]\) | \(-55486311952875723077768/801237030029296875\) | \(-48263544497109375000000000\) | \([2]\) | \(10321920\) | \(3.7329\) | |
| 23520.m2 | 23520bf3 | \([0, -1, 0, -313630641, 2111674775841]\) | \(7079962908642659949376/100085966990454375\) | \(48230457059164023866880000\) | \([2]\) | \(10321920\) | \(3.7329\) | |
| 23520.m1 | 23520bf4 | \([0, -1, 0, -5000940016, 136122808277716]\) | \(229625675762164624948320008/9568125\) | \(576348333120000\) | \([4]\) | \(10321920\) | \(3.7329\) |
Rank
sage: E.rank()
The elliptic curves in class 23520bf have rank \(1\).
Complex multiplication
The elliptic curves in class 23520bf do not have complex multiplication.Modular form 23520.2.a.bf
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
