Show commands:
SageMath
E = EllipticCurve("eg1")
E.isogeny_class()
Elliptic curves in class 352800.eg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 352800.eg1 | 352800eg1 | \([0, 0, 0, -334425, -67228000]\) | \(140608/15\) | \(441266692545000000\) | \([2]\) | \(3440640\) | \(2.1201\) | \(\Gamma_0(N)\)-optimal |
| 352800.eg2 | 352800eg2 | \([0, 0, 0, 437325, -331938250]\) | \(39304/225\) | \(-52952003105400000000\) | \([2]\) | \(6881280\) | \(2.4666\) |
Rank
sage: E.rank()
The elliptic curves in class 352800.eg have rank \(1\).
Complex multiplication
The elliptic curves in class 352800.eg do not have complex multiplication.Modular form 352800.2.a.eg
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.
