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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 32340.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
32340.c1 | 32340d2 | \([0, -1, 0, -11076, 452376]\) | \(1711503051568/7425\) | \(651974400\) | \([2]\) | \(32256\) | \(0.89810\) | |
32340.c2 | 32340d1 | \([0, -1, 0, -681, 7470]\) | \(-6373654528/441045\) | \(-2420454960\) | \([2]\) | \(16128\) | \(0.55152\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 32340.c have rank \(1\).
Complex multiplication
The elliptic curves in class 32340.c do not have complex multiplication.Modular form 32340.2.a.c
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.