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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 249090.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
249090.v1 | 249090v2 | \([1, 1, 0, -1960177662, -31678669709964]\) | \(17704693546393416119287921/1031232600000000000000\) | \(48515246182920600000000000000\) | \([2]\) | \(261273600\) | \(4.2579\) | |
249090.v2 | 249090v1 | \([1, 1, 0, -363229182, 2046646459764]\) | \(112653400663484247769201/26723840163840000000\) | \(1257246604211037143040000000\) | \([2]\) | \(130636800\) | \(3.9114\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 249090.v have rank \(1\).
Complex multiplication
The elliptic curves in class 249090.v do not have complex multiplication.Modular form 249090.2.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.