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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 46410.s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46410.s1 | 46410r4 | \([1, 1, 0, -125722, 17037406]\) | \(219767239605025443241/1009792505562750\) | \(1009792505562750\) | \([2]\) | \(442368\) | \(1.7298\) | |
| 46410.s2 | 46410r2 | \([1, 1, 0, -11972, -47844]\) | \(189793142380263241/109040585062500\) | \(109040585062500\) | \([2, 2]\) | \(221184\) | \(1.3832\) | |
| 46410.s3 | 46410r1 | \([1, 1, 0, -8592, -309456]\) | \(70159339776282121/183532986000\) | \(183532986000\) | \([2]\) | \(110592\) | \(1.0366\) | \(\Gamma_0(N)\)-optimal |
| 46410.s4 | 46410r3 | \([1, 1, 0, 47698, -322326]\) | \(12000794336358249239/6995491699218750\) | \(-6995491699218750\) | \([2]\) | \(442368\) | \(1.7298\) |
Rank
sage: E.rank()
The elliptic curves in class 46410.s have rank \(1\).
Complex multiplication
The elliptic curves in class 46410.s do not have complex multiplication.Modular form 46410.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
