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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 440818.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
440818.m1 | 440818m2 | \([1, 1, 0, -19194, -868102]\) | \(304821217/51842\) | \(133012388495378\) | \([2]\) | \(2384640\) | \(1.4308\) | |
440818.m2 | 440818m1 | \([1, 1, 0, -5504, 142220]\) | \(7189057/644\) | \(1652327807396\) | \([2]\) | \(1192320\) | \(1.0842\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 440818.m have rank \(0\).
Complex multiplication
The elliptic curves in class 440818.m do not have complex multiplication.Modular form 440818.2.a.m
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.