Show commands:
SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 75088t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 75088.w3 | 75088t1 | \([0, 1, 0, 2768, 92884]\) | \(12167/26\) | \(-5010198142976\) | \([]\) | \(114048\) | \(1.1211\) | \(\Gamma_0(N)\)-optimal |
| 75088.w2 | 75088t2 | \([0, 1, 0, -26112, -3245644]\) | \(-10218313/17576\) | \(-3386893944651776\) | \([]\) | \(342144\) | \(1.6704\) | |
| 75088.w1 | 75088t3 | \([0, 1, 0, -2654192, -1665243436]\) | \(-10730978619193/6656\) | \(-1282610724601856\) | \([]\) | \(1026432\) | \(2.2198\) |
Rank
sage: E.rank()
The elliptic curves in class 75088t have rank \(1\).
Complex multiplication
The elliptic curves in class 75088t do not have complex multiplication.Modular form 75088.2.a.t
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
