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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 24990h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24990.b4 | 24990h1 | \([1, 1, 0, 644717, 971744173]\) | \(251907898698209879/3611226931200000\) | \(-424857237228748800000\) | \([2]\) | \(1382400\) | \(2.6389\) | \(\Gamma_0(N)\)-optimal |
| 24990.b3 | 24990h2 | \([1, 1, 0, -11648403, 14349117357]\) | \(1485712211163154851241/103233690000000000\) | \(12145340394810000000000\) | \([2, 2]\) | \(2764800\) | \(2.9855\) | |
| 24990.b2 | 24990h3 | \([1, 1, 0, -36838323, -68833036467]\) | \(46993202771097749198761/9805297851562500000\) | \(1153583486938476562500000\) | \([2]\) | \(5529600\) | \(3.3320\) | |
| 24990.b1 | 24990h4 | \([1, 1, 0, -183148403, 953929017357]\) | \(5774905528848578698851241/31070538632700000\) | \(3655417799598522300000\) | \([2]\) | \(5529600\) | \(3.3320\) |
Rank
sage: E.rank()
The elliptic curves in class 24990h have rank \(1\).
Complex multiplication
The elliptic curves in class 24990h do not have complex multiplication.Modular form 24990.2.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.
