Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 15210d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15210.p3 | 15210d1 | \([1, -1, 0, -1299, 20853]\) | \(-1860867/320\) | \(-41703629760\) | \([2]\) | \(17280\) | \(0.76411\) | \(\Gamma_0(N)\)-optimal |
| 15210.p2 | 15210d2 | \([1, -1, 0, -21579, 1225485]\) | \(8527173507/200\) | \(26064768600\) | \([2]\) | \(34560\) | \(1.1107\) | |
| 15210.p4 | 15210d3 | \([1, -1, 0, 8841, -89335]\) | \(804357/500\) | \(-47503040773500\) | \([2]\) | \(51840\) | \(1.3134\) | |
| 15210.p1 | 15210d4 | \([1, -1, 0, -36789, -700777]\) | \(57960603/31250\) | \(2968940048343750\) | \([2]\) | \(103680\) | \(1.6600\) |
Rank
sage: E.rank()
The elliptic curves in class 15210d have rank \(0\).
Complex multiplication
The elliptic curves in class 15210d do not have complex multiplication.Modular form 15210.2.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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
