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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 53816.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 53816.d1 | 53816c4 | \([0, 0, 0, -287339, -59284090]\) | \(1443468546/7\) | \(12723252770816\) | \([2]\) | \(230400\) | \(1.7150\) | |
| 53816.d2 | 53816c3 | \([0, 0, 0, -56699, 4111158]\) | \(11090466/2401\) | \(4364075700389888\) | \([2]\) | \(230400\) | \(1.7150\) | |
| 53816.d3 | 53816c2 | \([0, 0, 0, -18259, -893730]\) | \(740772/49\) | \(44531384697856\) | \([2, 2]\) | \(115200\) | \(1.3684\) | |
| 53816.d4 | 53816c1 | \([0, 0, 0, 961, -59582]\) | \(432/7\) | \(-1590406596352\) | \([2]\) | \(57600\) | \(1.0218\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 53816.d have rank \(1\).
Complex multiplication
The elliptic curves in class 53816.d do not have complex multiplication.Modular form 53816.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
