Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 537.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
537.a1 | 537e1 | \([0, 1, 1, -340, 2308]\) | \(-4359504941056/10569771\) | \(-10569771\) | \([5]\) | \(192\) | \(0.22665\) | \(\Gamma_0(N)\)-optimal |
537.a2 | 537e2 | \([0, 1, 1, 2450, -39812]\) | \(1625716037832704/1653893972091\) | \(-1653893972091\) | \([]\) | \(960\) | \(1.0314\) |
Rank
sage: E.rank()
The elliptic curves in class 537.a have rank \(0\).
Complex multiplication
The elliptic curves in class 537.a do not have complex multiplication.Modular form 537.2.a.a
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.