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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 67600v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67600.ca2 | 67600v1 | \([0, 0, 0, -5915, 109850]\) | \(37044/13\) | \(8031810176000\) | \([2]\) | \(107520\) | \(1.1776\) | \(\Gamma_0(N)\)-optimal |
67600.ca1 | 67600v2 | \([0, 0, 0, -39715, -2965950]\) | \(5606442/169\) | \(208827064576000\) | \([2]\) | \(215040\) | \(1.5241\) |
Rank
sage: E.rank()
The elliptic curves in class 67600v have rank \(0\).
Complex multiplication
The elliptic curves in class 67600v do not have complex multiplication.Modular form 67600.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.