Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 334620i
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 334620.i2 | 334620i1 | \([0, 0, 0, 897, 1222]\) | \(2530736/1485\) | \(-46836092160\) | \([]\) | \(207360\) | \(0.73689\) | \(\Gamma_0(N)\)-optimal |
| 334620.i1 | 334620i2 | \([0, 0, 0, -13143, 610558]\) | \(-7960732624/499125\) | \(-15742130976000\) | \([]\) | \(622080\) | \(1.2862\) |
Rank
sage: E.rank()
The elliptic curves in class 334620i have rank \(1\).
Complex multiplication
The elliptic curves in class 334620i do not have complex multiplication.Modular form 334620.2.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.
