Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4900.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4900.f1 | 4900m2 | \([0, 1, 0, -4818, 127273]\) | \(-262885120/343\) | \(-16141442800\) | \([]\) | \(5184\) | \(0.86578\) | |
4900.f2 | 4900m1 | \([0, 1, 0, 82, 853]\) | \(1280/7\) | \(-329417200\) | \([]\) | \(1728\) | \(0.31647\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4900.f have rank \(1\).
Complex multiplication
The elliptic curves in class 4900.f do not have complex multiplication.Modular form 4900.2.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.