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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 116909c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116909.d2 | 116909c1 | \([1, -1, 1, -387592, -92628950]\) | \(43499078731809/82055753\) | \(12147196342919417\) | \([2]\) | \(1478400\) | \(1.9763\) | \(\Gamma_0(N)\)-optimal |
116909.d1 | 116909c2 | \([1, -1, 1, -6198657, -5938560340]\) | \(177930109857804849/634933\) | \(93992871110437\) | \([2]\) | \(2956800\) | \(2.3229\) |
Rank
sage: E.rank()
The elliptic curves in class 116909c have rank \(0\).
Complex multiplication
The elliptic curves in class 116909c do not have complex multiplication.Modular form 116909.2.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 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.