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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 9680.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9680.x1 | 9680y2 | \([0, 1, 0, -11499880, -15014090060]\) | \(-23178622194826561/1610510\) | \(-11686366028226560\) | \([]\) | \(288000\) | \(2.5372\) | |
| 9680.x2 | 9680y1 | \([0, 1, 0, 19320, -4165900]\) | \(109902239/1100000\) | \(-7981945241600000\) | \([]\) | \(57600\) | \(1.7325\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9680.x have rank \(0\).
Complex multiplication
The elliptic curves in class 9680.x do not have complex multiplication.Modular form 9680.2.a.x
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
