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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 20449.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20449.c1 | 20449f2 | \([1, 1, 1, -613896, 184886450]\) | \(-24729001\) | \(-1034669376040729\) | \([]\) | \(154440\) | \(1.9635\) | |
20449.c2 | 20449f1 | \([1, 1, 1, -426, -13408]\) | \(-121\) | \(-70669310569\) | \([]\) | \(14040\) | \(0.76451\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20449.c have rank \(0\).
Complex multiplication
The elliptic curves in class 20449.c do not have complex multiplication.Modular form 20449.2.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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.