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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 115920.ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 115920.ce1 | 115920cg1 | \([0, 0, 0, -597483, -173265318]\) | \(292583028222603/8456021875\) | \(681737742604800000\) | \([2]\) | \(1658880\) | \(2.1999\) | \(\Gamma_0(N)\)-optimal |
| 115920.ce2 | 115920cg2 | \([0, 0, 0, 143397, -574674102]\) | \(4044759171237/1771943359375\) | \(-142856852040000000000\) | \([2]\) | \(3317760\) | \(2.5465\) |
Rank
sage: E.rank()
The elliptic curves in class 115920.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 115920.ce do not have complex multiplication.Modular form 115920.2.a.ce
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.
