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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 129948h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 129948.l2 | 129948h1 | \([0, -1, 0, -154513, -23325686]\) | \(216727177216000/2738853\) | \(5155573065552\) | \([2]\) | \(414720\) | \(1.5855\) | \(\Gamma_0(N)\)-optimal |
| 129948.l3 | 129948h2 | \([0, -1, 0, -150348, -24646824]\) | \(-12479332642000/1526829993\) | \(-45985285592692992\) | \([2]\) | \(829440\) | \(1.9321\) | |
| 129948.l1 | 129948h3 | \([0, -1, 0, -242713, 6293638]\) | \(840033089536000/477272151837\) | \(898409462263539408\) | \([2]\) | \(1244160\) | \(2.1348\) | |
| 129948.l4 | 129948h4 | \([0, -1, 0, 960972, 49144824]\) | \(3258571509326000/1920843121977\) | \(-57852229749112850688\) | \([2]\) | \(2488320\) | \(2.4814\) |
Rank
sage: E.rank()
The elliptic curves in class 129948h have rank \(0\).
Complex multiplication
The elliptic curves in class 129948h do not have complex multiplication.Modular form 129948.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
