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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 16830.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16830.x1 | 16830bh4 | \([1, -1, 0, -1605834, 682139340]\) | \(628200507126935410849/88124751829125000\) | \(64242944083432125000\) | \([6]\) | \(663552\) | \(2.5270\) | |
| 16830.x2 | 16830bh2 | \([1, -1, 0, -410274, -100929132]\) | \(10476561483361670689/13992628953600\) | \(10200626507174400\) | \([2]\) | \(221184\) | \(1.9777\) | |
| 16830.x3 | 16830bh1 | \([1, -1, 0, -18594, -2460780]\) | \(-975276594443809/3037581803520\) | \(-2214397134766080\) | \([2]\) | \(110592\) | \(1.6311\) | \(\Gamma_0(N)\)-optimal |
| 16830.x4 | 16830bh3 | \([1, -1, 0, 162846, 57087828]\) | \(655127711084516831/2313151512408000\) | \(-1686287452545432000\) | \([6]\) | \(331776\) | \(2.1804\) |
Rank
sage: E.rank()
The elliptic curves in class 16830.x have rank \(1\).
Complex multiplication
The elliptic curves in class 16830.x do not have complex multiplication.Modular form 16830.2.a.x
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
