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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 417450.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
417450.c1 | 417450c2 | \([1, 1, 0, -5310450, 3341169000]\) | \(4786649882477/1374424524\) | \(4755618914378835937500\) | \([2]\) | \(46080000\) | \(2.8659\) | \(\Gamma_0(N)\)-optimal* |
417450.c2 | 417450c1 | \([1, 1, 0, -1982950, -1034493500]\) | \(249214435757/10820304\) | \(37439118309656250000\) | \([2]\) | \(23040000\) | \(2.5193\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 417450.c have rank \(1\).
Complex multiplication
The elliptic curves in class 417450.c do not have complex multiplication.Modular form 417450.2.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.