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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 75712.ba
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75712.ba1 | 75712cj1 | \([0, -1, 0, -1057, 14273]\) | \(-226981/14\) | \(-8063025152\) | \([]\) | \(46080\) | \(0.65530\) | \(\Gamma_0(N)\)-optimal |
| 75712.ba2 | 75712cj2 | \([0, -1, 0, 3103, -845183]\) | \(5735339/537824\) | \(-309749174239232\) | \([]\) | \(230400\) | \(1.4600\) |
Rank
sage: E.rank()
The elliptic curves in class 75712.ba have rank \(1\).
Complex multiplication
The elliptic curves in class 75712.ba do not have complex multiplication.Modular form 75712.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
