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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 7440.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7440.a1 | 7440k3 | \([0, -1, 0, -24216, 1396080]\) | \(383432500775449/18701300250\) | \(76600525824000\) | \([2]\) | \(27648\) | \(1.4237\) | |
| 7440.a2 | 7440k2 | \([0, -1, 0, -4216, -75920]\) | \(2023804595449/540562500\) | \(2214144000000\) | \([2, 2]\) | \(13824\) | \(1.0772\) | |
| 7440.a3 | 7440k1 | \([0, -1, 0, -3896, -92304]\) | \(1597099875769/186000\) | \(761856000\) | \([2]\) | \(6912\) | \(0.73058\) | \(\Gamma_0(N)\)-optimal |
| 7440.a4 | 7440k4 | \([0, -1, 0, 10664, -504464]\) | \(32740359775271/45410156250\) | \(-186000000000000\) | \([2]\) | \(27648\) | \(1.4237\) |
Rank
sage: E.rank()
The elliptic curves in class 7440.a have rank \(1\).
Complex multiplication
The elliptic curves in class 7440.a do not have complex multiplication.Modular form 7440.2.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.
