Show commands:
SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 7410.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7410.l1 | 7410l4 | \([1, 0, 1, -853958, 303669056]\) | \(68870385718115337310681/39076171875000\) | \(39076171875000\) | \([2]\) | \(73728\) | \(1.9342\) | |
7410.l2 | 7410l3 | \([1, 0, 1, -118678, -8887552]\) | \(184854108796733228761/72928592456733000\) | \(72928592456733000\) | \([2]\) | \(73728\) | \(1.9342\) | |
7410.l3 | 7410l2 | \([1, 0, 1, -53678, 4684448]\) | \(17104132791725468761/400280049000000\) | \(400280049000000\) | \([2, 2]\) | \(36864\) | \(1.5876\) | |
7410.l4 | 7410l1 | \([1, 0, 1, 402, 228256]\) | \(7210309838759/22505154048000\) | \(-22505154048000\) | \([2]\) | \(18432\) | \(1.2410\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7410.l have rank \(1\).
Complex multiplication
The elliptic curves in class 7410.l do not have complex multiplication.Modular form 7410.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.