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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 338130.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
338130.v1 | 338130v1 | \([1, -1, 0, -36715770, 85529961396]\) | \(63316050955793/93600000\) | \(8091772600046896800000\) | \([2]\) | \(36208640\) | \(3.1049\) | \(\Gamma_0(N)\)-optimal |
338130.v2 | 338130v2 | \([1, -1, 0, -26103690, 135977667300]\) | \(-22754202068753/79218750000\) | \(-6848505455768857968750000\) | \([2]\) | \(72417280\) | \(3.4515\) |
Rank
sage: E.rank()
The elliptic curves in class 338130.v have rank \(1\).
Complex multiplication
The elliptic curves in class 338130.v do not have complex multiplication.Modular form 338130.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.