Show commands:
SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 259182.fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259182.fe1 | 259182fe2 | \([1, -1, 1, -256664, -49588415]\) | \(53625283011/489566\) | \(17070987808209258\) | \([2]\) | \(2764800\) | \(1.9368\) | |
| 259182.fe2 | 259182fe1 | \([1, -1, 1, -27974, 540433]\) | \(69426531/36652\) | \(1278041867994276\) | \([2]\) | \(1382400\) | \(1.5902\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259182.fe have rank \(1\).
Complex multiplication
The elliptic curves in class 259182.fe do not have complex multiplication.Modular form 259182.2.a.fe
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.
