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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 19600.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19600.s1 | 19600bv2 | \([0, 1, 0, -143488, 20855988]\) | \(553463785/512\) | \(302241598668800\) | \([]\) | \(108864\) | \(1.7016\) | |
19600.s2 | 19600bv1 | \([0, 1, 0, -6288, -163052]\) | \(46585/8\) | \(4722524979200\) | \([]\) | \(36288\) | \(1.1523\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19600.s have rank \(2\).
Complex multiplication
The elliptic curves in class 19600.s do not have complex multiplication.Modular form 19600.2.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.