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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 20570.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20570.c1 | 20570b2 | \([1, 0, 1, -803564, 286126762]\) | \(-32391289681150609/1228250000000\) | \(-2175919798250000000\) | \([]\) | \(362880\) | \(2.2887\) | |
20570.c2 | 20570b1 | \([1, 0, 1, 48276, 1271466]\) | \(7023836099951/4456448000\) | \(-7894869475328000\) | \([]\) | \(120960\) | \(1.7394\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20570.c have rank \(1\).
Complex multiplication
The elliptic curves in class 20570.c do not have complex multiplication.Modular form 20570.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.