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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 13110.h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 13110.h1 | 13110g3 | \([1, 1, 0, -3687, 84651]\) | \(5545326987531001/89921490\) | \(89921490\) | \([2]\) | \(10240\) | \(0.65860\) | |
| 13110.h2 | 13110g2 | \([1, 1, 0, -237, 1161]\) | \(1481933914201/171872100\) | \(171872100\) | \([2, 2]\) | \(5120\) | \(0.31202\) | |
| 13110.h3 | 13110g1 | \([1, 1, 0, -57, -171]\) | \(21047437081/2831760\) | \(2831760\) | \([2]\) | \(2560\) | \(-0.034549\) | \(\Gamma_0(N)\)-optimal |
| 13110.h4 | 13110g4 | \([1, 1, 0, 333, 6519]\) | \(4064592619079/19938671250\) | \(-19938671250\) | \([2]\) | \(10240\) | \(0.65860\) |
Rank
sage: E.rank()
The elliptic curves in class 13110.h have rank \(1\).
Complex multiplication
The elliptic curves in class 13110.h do not have complex multiplication.Modular form 13110.2.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.
