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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 203280d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
203280.go1 | 203280d1 | \([0, 1, 0, -9670360, -11577477100]\) | \(13782741913468081/701662500\) | \(5091483320985600000\) | \([2]\) | \(8294400\) | \(2.6595\) | \(\Gamma_0(N)\)-optimal |
203280.go2 | 203280d2 | \([0, 1, 0, -9147640, -12884068012]\) | \(-11666347147400401/3126621093750\) | \(-22687743965040000000000\) | \([2]\) | \(16588800\) | \(3.0061\) |
Rank
sage: E.rank()
The elliptic curves in class 203280d have rank \(0\).
Complex multiplication
The elliptic curves in class 203280d do not have complex multiplication.Modular form 203280.2.a.d
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.