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SageMath
E = EllipticCurve("gh1")
E.isogeny_class()
Elliptic curves in class 33600gh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.dy3 | 33600gh1 | \([0, 1, 0, -5633, 100863]\) | \(4826809/1680\) | \(6881280000000\) | \([2]\) | \(73728\) | \(1.1649\) | \(\Gamma_0(N)\)-optimal |
| 33600.dy2 | 33600gh2 | \([0, 1, 0, -37633, -2747137]\) | \(1439069689/44100\) | \(180633600000000\) | \([2, 2]\) | \(147456\) | \(1.5114\) | |
| 33600.dy4 | 33600gh3 | \([0, 1, 0, 10367, -9227137]\) | \(30080231/9003750\) | \(-36879360000000000\) | \([2]\) | \(294912\) | \(1.8580\) | |
| 33600.dy1 | 33600gh4 | \([0, 1, 0, -597633, -178027137]\) | \(5763259856089/5670\) | \(23224320000000\) | \([2]\) | \(294912\) | \(1.8580\) |
Rank
sage: E.rank()
The elliptic curves in class 33600gh have rank \(1\).
Complex multiplication
The elliptic curves in class 33600gh do not have complex multiplication.Modular form 33600.2.a.gh
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
