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SageMath
E = EllipticCurve("mi1")
E.isogeny_class()
Elliptic curves in class 487872.mi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.mi1 | 487872mi2 | \([0, 0, 0, -1709004, 713778032]\) | \(2450086/441\) | \(99359686031035465728\) | \([2]\) | \(10813440\) | \(2.5562\) | \(\Gamma_0(N)\)-optimal* |
487872.mi2 | 487872mi1 | \([0, 0, 0, 207636, 64420400]\) | \(8788/21\) | \(-2365706810262749184\) | \([2]\) | \(5406720\) | \(2.2096\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 487872.mi have rank \(0\).
Complex multiplication
The elliptic curves in class 487872.mi do not have complex multiplication.Modular form 487872.2.a.mi
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.