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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 10608.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10608.q1 | 10608z3 | \([0, 1, 0, -17464, -894124]\) | \(143820170742457/5826444\) | \(23865114624\) | \([2]\) | \(12288\) | \(1.0736\) | |
| 10608.q2 | 10608z4 | \([0, 1, 0, -5304, 135252]\) | \(4029546653497/351790452\) | \(1440933691392\) | \([4]\) | \(12288\) | \(1.0736\) | |
| 10608.q3 | 10608z2 | \([0, 1, 0, -1144, -12844]\) | \(40459583737/7033104\) | \(28807593984\) | \([2, 2]\) | \(6144\) | \(0.72702\) | |
| 10608.q4 | 10608z1 | \([0, 1, 0, 136, -1068]\) | \(67419143/169728\) | \(-695205888\) | \([2]\) | \(3072\) | \(0.38045\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 10608.q have rank \(1\).
Complex multiplication
The elliptic curves in class 10608.q do not have complex multiplication.Modular form 10608.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
