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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 3136.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3136.s1 | 3136o2 | \([0, 1, 0, -27897, 1784159]\) | \(406749952\) | \(5903156224\) | \([]\) | \(4032\) | \(1.1145\) | |
3136.s2 | 3136o1 | \([0, 1, 0, -457, 559]\) | \(1792\) | \(5903156224\) | \([]\) | \(1344\) | \(0.56519\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3136.s have rank \(0\).
Complex multiplication
The elliptic curves in class 3136.s do not have complex multiplication.Modular form 3136.2.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.