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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 127296.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 127296.v1 | 127296cf4 | \([0, 0, 0, -85836, -9675344]\) | \(2927889364616/1449981\) | \(34636960530432\) | \([2]\) | \(393216\) | \(1.5512\) | |
| 127296.v2 | 127296cf3 | \([0, 0, 0, -48396, 4031440]\) | \(524776831496/9771957\) | \(233431258005504\) | \([2]\) | \(393216\) | \(1.5512\) | |
| 127296.v3 | 127296cf2 | \([0, 0, 0, -6276, -96320]\) | \(9155562688/3956121\) | \(11812914008064\) | \([2, 2]\) | \(196608\) | \(1.2046\) | |
| 127296.v4 | 127296cf1 | \([0, 0, 0, 1329, -11144]\) | \(5564051648/4369833\) | \(-203878928448\) | \([2]\) | \(98304\) | \(0.85804\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 127296.v have rank \(1\).
Complex multiplication
The elliptic curves in class 127296.v do not have complex multiplication.Modular form 127296.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
