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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 59976bi
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 59976.bf2 | 59976bi1 | \([0, 0, 0, -2660259, 17428560590]\) | \(-23707171994692/1480419781911\) | \(-130017138837680575724544\) | \([2]\) | \(6488064\) | \(3.1150\) | \(\Gamma_0(N)\)-optimal |
| 59976.bf1 | 59976bi2 | \([0, 0, 0, -118396299, 492663888038]\) | \(1044942448578893426/7759962920241\) | \(1363029849646905252169728\) | \([2]\) | \(12976128\) | \(3.4615\) |
Rank
sage: E.rank()
The elliptic curves in class 59976bi have rank \(0\).
Complex multiplication
The elliptic curves in class 59976bi do not have complex multiplication.Modular form 59976.2.a.bi
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.
