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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 94640.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
94640.s1 | 94640bp1 | \([0, -1, 0, -26902907256, -1698418228173200]\) | \(-644487634439863642624729/896000\) | \(-2993744797761536000\) | \([]\) | \(64696320\) | \(4.1945\) | \(\Gamma_0(N)\)-optimal |
94640.s2 | 94640bp2 | \([0, -1, 0, -26895701096, -1699373573481104]\) | \(-643969879566315506524489/719323136000000000\) | \(-2403426223559725285376000000000\) | \([]\) | \(194088960\) | \(4.7438\) |
Rank
sage: E.rank()
The elliptic curves in class 94640.s have rank \(0\).
Complex multiplication
The elliptic curves in class 94640.s do not have complex multiplication.Modular form 94640.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.