Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 28880q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28880.ba2 | 28880q1 | \([0, -1, 0, -585301, -172098915]\) | \(318767104/125\) | \(8695584276992000\) | \([]\) | \(344736\) | \(2.0231\) | \(\Gamma_0(N)\)-optimal |
| 28880.ba1 | 28880q2 | \([0, -1, 0, -1682741, 626178941]\) | \(7575076864/1953125\) | \(135868504328000000000\) | \([]\) | \(1034208\) | \(2.5724\) |
Rank
sage: E.rank()
The elliptic curves in class 28880q have rank \(0\).
Complex multiplication
The elliptic curves in class 28880q do not have complex multiplication.Modular form 28880.2.a.q
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.
