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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 19573.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19573.c1 | 19573a3 | \([0, 1, 1, -990993, 379381573]\) | \(727057727488000/37\) | \(5477327893\) | \([]\) | \(71280\) | \(1.7898\) | |
19573.c2 | 19573a2 | \([0, 1, 1, -12343, 507012]\) | \(1404928000/50653\) | \(7498461885517\) | \([]\) | \(23760\) | \(1.2405\) | |
19573.c3 | 19573a1 | \([0, 1, 1, -1763, -28865]\) | \(4096000/37\) | \(5477327893\) | \([]\) | \(7920\) | \(0.69122\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 19573.c have rank \(2\).
Complex multiplication
The elliptic curves in class 19573.c do not have complex multiplication.Modular form 19573.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.