Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 137904.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 137904.w1 | 137904da2 | \([0, -1, 0, -261668, -23192352]\) | \(1603530178000/738501777\) | \(912539398077335808\) | \([2]\) | \(1548288\) | \(2.1410\) | |
| 137904.w2 | 137904da1 | \([0, -1, 0, -132383, 18333990]\) | \(3322336000000/51429573\) | \(3971851613160912\) | \([2]\) | \(774144\) | \(1.7944\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 137904.w have rank \(0\).
Complex multiplication
The elliptic curves in class 137904.w do not have complex multiplication.Modular form 137904.2.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.
