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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 15918.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
15918.w1 | 15918w2 | \([1, 0, 0, -37076386, -86899858498]\) | \(-5636582885237244926059353889/141528862087790972634\) | \(-141528862087790972634\) | \([]\) | \(1152480\) | \(2.9749\) | |
15918.w2 | 15918w1 | \([1, 0, 0, 110624, 15558272]\) | \(149717146211547812351/191087828767269504\) | \(-191087828767269504\) | \([7]\) | \(164640\) | \(2.0019\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 15918.w have rank \(1\).
Complex multiplication
The elliptic curves in class 15918.w do not have complex multiplication.Modular form 15918.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.