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SageMath
E = EllipticCurve("is1")
E.isogeny_class()
Elliptic curves in class 129600.is
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129600.is1 | 129600cb1 | \([0, 0, 0, -9900, 414000]\) | \(-35937/4\) | \(-11943936000000\) | \([]\) | \(248832\) | \(1.2466\) | \(\Gamma_0(N)\)-optimal |
| 129600.is2 | 129600cb2 | \([0, 0, 0, 62100, -594000]\) | \(109503/64\) | \(-15479341056000000\) | \([]\) | \(746496\) | \(1.7959\) |
Rank
sage: E.rank()
The elliptic curves in class 129600.is have rank \(1\).
Complex multiplication
The elliptic curves in class 129600.is do not have complex multiplication.Modular form 129600.2.a.is
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
