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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 377520c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 377520.c2 | 377520c1 | \([0, -1, 0, 1104, -4464]\) | \(109083604/68445\) | \(-93286702080\) | \([2]\) | \(430080\) | \(0.79397\) | \(\Gamma_0(N)\)-optimal |
| 377520.c1 | 377520c2 | \([0, -1, 0, -4616, -31920]\) | \(3991233958/2132325\) | \(5812479129600\) | \([2]\) | \(860160\) | \(1.1405\) |
Rank
sage: E.rank()
The elliptic curves in class 377520c have rank \(1\).
Complex multiplication
The elliptic curves in class 377520c do not have complex multiplication.Modular form 377520.2.a.c
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
