Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 7488.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7488.s1 | 7488bi2 | \([0, 0, 0, -36396, 2671056]\) | \(1033364331/676\) | \(3488011517952\) | \([2]\) | \(18432\) | \(1.3464\) | |
| 7488.s2 | 7488bi1 | \([0, 0, 0, -1836, 58320]\) | \(-132651/208\) | \(-1073234313216\) | \([2]\) | \(9216\) | \(0.99980\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7488.s have rank \(1\).
Complex multiplication
The elliptic curves in class 7488.s do not have complex multiplication.Modular form 7488.2.a.s
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
