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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 33488h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33488.o4 | 33488h1 | \([0, 0, 0, -146, -1185]\) | \(-21511084032/25465531\) | \(-407448496\) | \([2]\) | \(8192\) | \(0.34605\) | \(\Gamma_0(N)\)-optimal |
| 33488.o3 | 33488h2 | \([0, 0, 0, -2791, -56730]\) | \(9392111857872/4380649\) | \(1121446144\) | \([2, 2]\) | \(16384\) | \(0.69262\) | |
| 33488.o2 | 33488h3 | \([0, 0, 0, -3251, -36766]\) | \(3710860803108/1577224103\) | \(1615077481472\) | \([4]\) | \(32768\) | \(1.0392\) | |
| 33488.o1 | 33488h4 | \([0, 0, 0, -44651, -3631574]\) | \(9614292367656708/2093\) | \(2143232\) | \([2]\) | \(32768\) | \(1.0392\) |
Rank
sage: E.rank()
The elliptic curves in class 33488h have rank \(1\).
Complex multiplication
The elliptic curves in class 33488h do not have complex multiplication.Modular form 33488.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
