Show commands:
SageMath
E = EllipticCurve("gu1")
E.isogeny_class()
Elliptic curves in class 129600gu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129600.r2 | 129600gu1 | \([0, 0, 0, 6900, -22000]\) | \(109503/64\) | \(-21233664000000\) | \([]\) | \(248832\) | \(1.2466\) | \(\Gamma_0(N)\)-optimal |
| 129600.r1 | 129600gu2 | \([0, 0, 0, -89100, 11178000]\) | \(-35937/4\) | \(-8707129344000000\) | \([]\) | \(746496\) | \(1.7959\) |
Rank
sage: E.rank()
The elliptic curves in class 129600gu have rank \(0\).
Complex multiplication
The elliptic curves in class 129600gu do not have complex multiplication.Modular form 129600.2.a.gu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
