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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 47432.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47432.c1 | 47432z2 | \([0, 1, 0, -135135744, 424047903376]\) | \(1278763167594532/375974556419\) | \(80242188187396088567081984\) | \([2]\) | \(11059200\) | \(3.6764\) | |
47432.c2 | 47432z1 | \([0, 1, 0, 22694236, 44119575520]\) | \(24226243449392/29774625727\) | \(-1588658780231811059123968\) | \([2]\) | \(5529600\) | \(3.3299\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 47432.c have rank \(0\).
Complex multiplication
The elliptic curves in class 47432.c do not have complex multiplication.Modular form 47432.2.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.