Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 53130h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
53130.h1 | 53130h1 | \([1, 1, 0, -468250148, 3584540196252]\) | \(11354224670262535781399662607689/1019390529976200592619062500\) | \(1019390529976200592619062500\) | \([2]\) | \(33868800\) | \(3.9221\) | \(\Gamma_0(N)\)-optimal |
53130.h2 | 53130h2 | \([1, 1, 0, 528236882, 16794171563338]\) | \(16300835816496943562017955390231/131273254164601244421386718750\) | \(-131273254164601244421386718750\) | \([2]\) | \(67737600\) | \(4.2687\) |
Rank
sage: E.rank()
The elliptic curves in class 53130h have rank \(0\).
Complex multiplication
The elliptic curves in class 53130h do not have complex multiplication.Modular form 53130.2.a.h
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.