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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 24150f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 24150.h3 | 24150f1 | \([1, 1, 0, -18900, -1008000]\) | \(47788676405569/579600\) | \(9056250000\) | \([2]\) | \(49152\) | \(1.0591\) | \(\Gamma_0(N)\)-optimal |
| 24150.h2 | 24150f2 | \([1, 1, 0, -19400, -952500]\) | \(51682540549249/5249002500\) | \(82015664062500\) | \([2, 2]\) | \(98304\) | \(1.4057\) | |
| 24150.h4 | 24150f3 | \([1, 1, 0, 24350, -4583750]\) | \(102181603702751/642612880350\) | \(-10040826255468750\) | \([2]\) | \(196608\) | \(1.7523\) | |
| 24150.h1 | 24150f4 | \([1, 1, 0, -71150, 6240750]\) | \(2549399737314529/388286718750\) | \(6066979980468750\) | \([2]\) | \(196608\) | \(1.7523\) |
Rank
sage: E.rank()
The elliptic curves in class 24150f have rank \(0\).
Complex multiplication
The elliptic curves in class 24150f do not have complex multiplication.Modular form 24150.2.a.f
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.
