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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2415.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2415.a1 | 2415a3 | \([1, 1, 1, -5051, 136064]\) | \(14251520160844849/264449745\) | \(264449745\) | \([2]\) | \(1920\) | \(0.74103\) | |
| 2415.a2 | 2415a2 | \([1, 1, 1, -326, 1874]\) | \(3832302404449/472410225\) | \(472410225\) | \([2, 2]\) | \(960\) | \(0.39445\) | |
| 2415.a3 | 2415a1 | \([1, 1, 1, -81, -282]\) | \(58818484369/7455105\) | \(7455105\) | \([2]\) | \(480\) | \(0.047881\) | \(\Gamma_0(N)\)-optimal |
| 2415.a4 | 2415a4 | \([1, 1, 1, 479, 10568]\) | \(12152722588271/53476250625\) | \(-53476250625\) | \([2]\) | \(1920\) | \(0.74103\) |
Rank
sage: E.rank()
The elliptic curves in class 2415.a have rank \(1\).
Complex multiplication
The elliptic curves in class 2415.a do not have complex multiplication.Modular form 2415.2.a.a
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.
