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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 128797.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
128797.a1 | 128797a3 | \([0, 1, 1, -6521073, 6407364502]\) | \(727057727488000/37\) | \(1560679744717\) | \([]\) | \(1202688\) | \(2.2608\) | |
128797.a2 | 128797a2 | \([0, 1, 1, -81223, 8600745]\) | \(1404928000/50653\) | \(2136570570517573\) | \([]\) | \(400896\) | \(1.7115\) | |
128797.a3 | 128797a1 | \([0, 1, 1, -11603, -481184]\) | \(4096000/37\) | \(1560679744717\) | \([]\) | \(133632\) | \(1.1622\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 128797.a have rank \(2\).
Complex multiplication
The elliptic curves in class 128797.a do not have complex multiplication.Modular form 128797.2.a.a
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.