Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 209484u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 209484.ba2 | 209484u1 | \([0, 0, 0, -345, 1357]\) | \(736000/297\) | \(1832566032\) | \([]\) | \(82944\) | \(0.47533\) | \(\Gamma_0(N)\)-optimal |
| 209484.ba1 | 209484u2 | \([0, 0, 0, -12765, -555059]\) | \(37280608000/3993\) | \(24637832208\) | \([]\) | \(248832\) | \(1.0246\) |
Rank
sage: E.rank()
The elliptic curves in class 209484u have rank \(0\).
Complex multiplication
The elliptic curves in class 209484u do not have complex multiplication.Modular form 209484.2.a.u
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.
