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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 35904.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35904.h1 | 35904k4 | \([0, -1, 0, -11649, -478335]\) | \(666940371553/2756193\) | \(722519457792\) | \([2]\) | \(65536\) | \(1.1308\) | |
| 35904.h2 | 35904k2 | \([0, -1, 0, -1089, 1089]\) | \(545338513/314721\) | \(82502221824\) | \([2, 2]\) | \(32768\) | \(0.78420\) | |
| 35904.h3 | 35904k1 | \([0, -1, 0, -769, 8449]\) | \(192100033/561\) | \(147062784\) | \([2]\) | \(16384\) | \(0.43763\) | \(\Gamma_0(N)\)-optimal |
| 35904.h4 | 35904k3 | \([0, -1, 0, 4351, 4353]\) | \(34741712447/20160657\) | \(-5284995268608\) | \([2]\) | \(65536\) | \(1.1308\) |
Rank
sage: E.rank()
The elliptic curves in class 35904.h have rank \(2\).
Complex multiplication
The elliptic curves in class 35904.h do not have complex multiplication.Modular form 35904.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
