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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 37485b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 37485.k2 | 37485b1 | \([1, -1, 1, -83, 5562]\) | \(-19683/4165\) | \(-13230218295\) | \([2]\) | \(18432\) | \(0.62143\) | \(\Gamma_0(N)\)-optimal |
| 37485.k1 | 37485b2 | \([1, -1, 1, -5228, 145506]\) | \(4973940243/50575\) | \(160652650725\) | \([2]\) | \(36864\) | \(0.96800\) |
Rank
sage: E.rank()
The elliptic curves in class 37485b have rank \(2\).
Complex multiplication
The elliptic curves in class 37485b do not have complex multiplication.Modular form 37485.2.a.b
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.
