Show commands:
SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 94640bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 94640.l2 | 94640bl1 | \([0, 1, 0, -15240, 691588]\) | \(174011157652/7503125\) | \(16879990400000\) | \([2]\) | \(245760\) | \(1.3019\) | \(\Gamma_0(N)\)-optimal |
| 94640.l1 | 94640bl2 | \([0, 1, 0, -40720, -2253900]\) | \(1659578027546/478515625\) | \(2153060000000000\) | \([2]\) | \(491520\) | \(1.6485\) |
Rank
sage: E.rank()
The elliptic curves in class 94640bl have rank \(2\).
Complex multiplication
The elliptic curves in class 94640bl do not have complex multiplication.Modular form 94640.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
