Show commands:
SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 102960.dj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 102960.dj1 | 102960ea4 | \([0, 0, 0, -23101347, -42735989086]\) | \(456612868287073618849/12544848030000\) | \(37458715500011520000\) | \([2]\) | \(4718592\) | \(2.8592\) | |
| 102960.dj2 | 102960ea3 | \([0, 0, 0, -6443427, 5691459746]\) | \(9908022260084596129/1047363281250000\) | \(3127410000000000000000\) | \([4]\) | \(4718592\) | \(2.8592\) | |
| 102960.dj3 | 102960ea2 | \([0, 0, 0, -1501347, -611669086]\) | \(125337052492018849/18404100000000\) | \(54954348134400000000\) | \([2, 2]\) | \(2359296\) | \(2.5126\) | |
| 102960.dj4 | 102960ea1 | \([0, 0, 0, 157533, -51962974]\) | \(144794100308831/474439680000\) | \(-1416669293445120000\) | \([2]\) | \(1179648\) | \(2.1660\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 102960.dj have rank \(1\).
Complex multiplication
The elliptic curves in class 102960.dj do not have complex multiplication.Modular form 102960.2.a.dj
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.
