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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 1088.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1088.h1 | 1088k3 | \([0, 0, 0, -5804, 170192]\) | \(82483294977/17\) | \(4456448\) | \([2]\) | \(512\) | \(0.66308\) | |
| 1088.h2 | 1088k2 | \([0, 0, 0, -364, 2640]\) | \(20346417/289\) | \(75759616\) | \([2, 2]\) | \(256\) | \(0.31651\) | |
| 1088.h3 | 1088k1 | \([0, 0, 0, -44, -48]\) | \(35937/17\) | \(4456448\) | \([2]\) | \(128\) | \(-0.030063\) | \(\Gamma_0(N)\)-optimal |
| 1088.h4 | 1088k4 | \([0, 0, 0, -44, 7120]\) | \(-35937/83521\) | \(-21894529024\) | \([2]\) | \(512\) | \(0.66308\) |
Rank
sage: E.rank()
The elliptic curves in class 1088.h have rank \(1\).
Complex multiplication
The elliptic curves in class 1088.h do not have complex multiplication.Modular form 1088.2.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.
