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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 311696j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
311696.j2 | 311696j1 | \([0, 1, 0, -11578288, -53325652140]\) | \(-23655968592999625/155579103523228\) | \(-1128930804599657754247168\) | \([2]\) | \(33177600\) | \(3.2987\) | \(\Gamma_0(N)\)-optimal |
311696.j1 | 311696j2 | \([0, 1, 0, -295028048, -1946429909228]\) | \(391379047744832043625/964051690355138\) | \(6995461638624209430192128\) | \([2]\) | \(66355200\) | \(3.6453\) |
Rank
sage: E.rank()
The elliptic curves in class 311696j have rank \(1\).
Complex multiplication
The elliptic curves in class 311696j do not have complex multiplication.Modular form 311696.2.a.j
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 Cremona 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 Cremona labels.