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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 13950.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13950.m1 | 13950z2 | \([1, -1, 0, -8424567, -8777770659]\) | \(5805223604235668521/435937500000000\) | \(4965600585937500000000\) | \([2]\) | \(1032192\) | \(2.9084\) | |
13950.m2 | 13950z1 | \([1, -1, 0, 503433, -608650659]\) | \(1238798620042199/14760960000000\) | \(-168136560000000000000\) | \([2]\) | \(516096\) | \(2.5618\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13950.m have rank \(1\).
Complex multiplication
The elliptic curves in class 13950.m do not have complex multiplication.Modular form 13950.2.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.