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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 13923c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13923.c2 | 13923c1 | \([1, -1, 1, -296, 2010]\) | \(105890949891/1288651\) | \(34793577\) | \([2]\) | \(3840\) | \(0.25772\) | \(\Gamma_0(N)\)-optimal |
13923.c1 | 13923c2 | \([1, -1, 1, -551, -1764]\) | \(684030715731/338005577\) | \(9126150579\) | \([2]\) | \(7680\) | \(0.60429\) |
Rank
sage: E.rank()
The elliptic curves in class 13923c have rank \(2\).
Complex multiplication
The elliptic curves in class 13923c do not have complex multiplication.Modular form 13923.2.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.