Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 57475.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57475.f1 | 57475g1 | \([0, -1, 1, -82683, -10674357]\) | \(-2258403328/480491\) | \(-13300298694546875\) | \([]\) | \(311040\) | \(1.8153\) | \(\Gamma_0(N)\)-optimal |
| 57475.f2 | 57475g2 | \([0, -1, 1, 582817, 61698768]\) | \(790939860992/517504691\) | \(-14324861373322671875\) | \([]\) | \(933120\) | \(2.3646\) |
Rank
sage: E.rank()
The elliptic curves in class 57475.f have rank \(0\).
Complex multiplication
The elliptic curves in class 57475.f do not have complex multiplication.Modular form 57475.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
