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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 115920.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.be1 | 115920cj2 | \([0, 0, 0, -573407883, 925493135418]\) | \(258620799050621485981803/145075171220000000000\) | \(11696187781624872960000000000\) | \([2]\) | \(60825600\) | \(4.0759\) | |
| 115920.be2 | 115920cj1 | \([0, 0, 0, -356647563, -2578610845638]\) | \(62228632040416581492843/382900201062400000\) | \(30870014597165953843200000\) | \([2]\) | \(30412800\) | \(3.7294\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 115920.be have rank \(0\).
Complex multiplication
The elliptic curves in class 115920.be do not have complex multiplication.Modular form 115920.2.a.be
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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
