Show commands:
SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 30324h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 30324.h2 | 30324h1 | \([0, 1, 0, 89047, 10865124]\) | \(103737344000/127413867\) | \(-95908761994109232\) | \([2]\) | \(311040\) | \(1.9446\) | \(\Gamma_0(N)\)-optimal |
| 30324.h1 | 30324h2 | \([0, 1, 0, -530068, 103980020]\) | \(1367595682000/402300927\) | \(4845209993684911872\) | \([2]\) | \(622080\) | \(2.2912\) |
Rank
sage: E.rank()
The elliptic curves in class 30324h have rank \(0\).
Complex multiplication
The elliptic curves in class 30324h do not have complex multiplication.Modular form 30324.2.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.
