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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 11858.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11858.c1 | 11858r2 | \([1, 0, 1, -338077, 29617410]\) | \(59776471/29282\) | \(2093337277881771614\) | \([2]\) | \(215040\) | \(2.2087\) | |
11858.c2 | 11858r1 | \([1, 0, 1, 76953, 3553526]\) | \(704969/484\) | \(-34600616163335068\) | \([2]\) | \(107520\) | \(1.8622\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11858.c have rank \(1\).
Complex multiplication
The elliptic curves in class 11858.c do not have complex multiplication.Modular form 11858.2.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.