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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 10010.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10010.q1 | 10010m3 | \([1, -1, 1, -2293, 38607]\) | \(1332779492447649/146356560350\) | \(146356560350\) | \([2]\) | \(14336\) | \(0.87593\) | |
| 10010.q2 | 10010m2 | \([1, -1, 1, -543, -4093]\) | \(17675559395649/2505002500\) | \(2505002500\) | \([2, 2]\) | \(7168\) | \(0.52936\) | |
| 10010.q3 | 10010m1 | \([1, -1, 1, -523, -4469]\) | \(15792469779969/400400\) | \(400400\) | \([2]\) | \(3584\) | \(0.18278\) | \(\Gamma_0(N)\)-optimal |
| 10010.q4 | 10010m4 | \([1, -1, 1, 887, -22969]\) | \(77259787831071/268236718750\) | \(-268236718750\) | \([2]\) | \(14336\) | \(0.87593\) |
Rank
sage: E.rank()
The elliptic curves in class 10010.q have rank \(0\).
Complex multiplication
The elliptic curves in class 10010.q do not have complex multiplication.Modular form 10010.2.a.q
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.
