Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 2576.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2576.e1 | 2576c2 | \([0, 1, 0, -2672, -51212]\) | \(1030541881826/62236321\) | \(127459985408\) | \([2]\) | \(1920\) | \(0.88336\) | |
2576.e2 | 2576c1 | \([0, 1, 0, -2632, -52860]\) | \(1969910093092/7889\) | \(8078336\) | \([2]\) | \(960\) | \(0.53679\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2576.e have rank \(1\).
Complex multiplication
The elliptic curves in class 2576.e do not have complex multiplication.Modular form 2576.2.a.e
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.