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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 19600cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19600.dv2 | 19600cu1 | \([0, -1, 0, -1392008, 743862512]\) | \(-115501303/25600\) | \(-66115349708800000000\) | \([2]\) | \(645120\) | \(2.5236\) | \(\Gamma_0(N)\)-optimal |
| 19600.dv1 | 19600cu2 | \([0, -1, 0, -23344008, 43418550512]\) | \(544737993463/20000\) | \(51652616960000000000\) | \([2]\) | \(1290240\) | \(2.8702\) |
Rank
sage: E.rank()
The elliptic curves in class 19600cu have rank \(1\).
Complex multiplication
The elliptic curves in class 19600cu do not have complex multiplication.Modular form 19600.2.a.cu
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.
