Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 72450.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 72450.w1 | 72450a1 | \([1, -1, 0, -123165042, -219939523884]\) | \(489781415227546051766883/233890092903563264000\) | \(98672382943690752000000000\) | \([2]\) | \(24772608\) | \(3.6817\) | \(\Gamma_0(N)\)-optimal |
| 72450.w2 | 72450a2 | \([1, -1, 0, 442082958, -1673192131884]\) | \(22649115256119592694355357/15973509811739648000000\) | \(-6738824451827664000000000000\) | \([2]\) | \(49545216\) | \(4.0283\) |
Rank
sage: E.rank()
The elliptic curves in class 72450.w have rank \(1\).
Complex multiplication
The elliptic curves in class 72450.w do not have complex multiplication.Modular form 72450.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
