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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 71478bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 71478.m1 | 71478bd1 | \([1, -1, 0, -47615787, 107471141253]\) | \(348118804674069625/56004830035968\) | \(1920766699017787284652032\) | \([2]\) | \(14376960\) | \(3.3818\) | \(\Gamma_0(N)\)-optimal |
| 71478.m2 | 71478bd2 | \([1, -1, 0, 85463253, 600369289605]\) | \(2012856588372458375/5705334819790848\) | \(-195672714684839739644977152\) | \([2]\) | \(28753920\) | \(3.7284\) |
Rank
sage: E.rank()
The elliptic curves in class 71478bd have rank \(0\).
Complex multiplication
The elliptic curves in class 71478bd do not have complex multiplication.Modular form 71478.2.a.bd
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.
