Show commands:
SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 57498e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
57498.e2 | 57498e1 | \([1, 1, 0, 3233550, -168288588]\) | \(1457309849609375/848195776512\) | \(-2176238303799100305408\) | \([2]\) | \(3939840\) | \(2.7838\) | \(\Gamma_0(N)\)-optimal |
57498.e1 | 57498e2 | \([1, 1, 0, -12975410, -1364509836]\) | \(94162220003958625/54181012560192\) | \(139013654792045316510528\) | \([2]\) | \(7879680\) | \(3.1303\) |
Rank
sage: E.rank()
The elliptic curves in class 57498e have rank \(0\).
Complex multiplication
The elliptic curves in class 57498e do not have complex multiplication.Modular form 57498.2.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 Cremona 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 Cremona labels.