Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 309738i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 309738.i1 | 309738i1 | \([1, 1, 0, -91340, -19394736]\) | \(-1791399948625/2403827712\) | \(-113090192483254272\) | \([]\) | \(3110400\) | \(1.9650\) | \(\Gamma_0(N)\)-optimal |
| 309738.i2 | 309738i2 | \([1, 1, 0, 775060, 375441072]\) | \(1094478419891375/1925485038048\) | \(-90586139967286680288\) | \([]\) | \(9331200\) | \(2.5143\) |
Rank
sage: E.rank()
The elliptic curves in class 309738i have rank \(0\).
Complex multiplication
The elliptic curves in class 309738i do not have complex multiplication.Modular form 309738.2.a.i
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.
