Show commands:
SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 349830s
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 349830.s2 | 349830s1 | \([1, -1, 0, 495, -5589]\) | \(108750551/167670\) | \(-20657111670\) | \([]\) | \(248832\) | \(0.66457\) | \(\Gamma_0(N)\)-optimal |
| 349830.s1 | 349830s2 | \([1, -1, 0, -4770, 218700]\) | \(-97435188409/109503000\) | \(-13490879103000\) | \([]\) | \(746496\) | \(1.2139\) |
Rank
sage: E.rank()
The elliptic curves in class 349830s have rank \(1\).
Complex multiplication
The elliptic curves in class 349830s do not have complex multiplication.Modular form 349830.2.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 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.
