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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 82810.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82810.q1 | 82810e4 | \([1, -1, 0, -2216720, 1270815846]\) | \(2121328796049/120050\) | \(68172703707522050\) | \([2]\) | \(1474560\) | \(2.2944\) | |
| 82810.q2 | 82810e3 | \([1, -1, 0, -726140, -222380950]\) | \(74565301329/5468750\) | \(3105534972099218750\) | \([2]\) | \(1474560\) | \(2.2944\) | |
| 82810.q3 | 82810e2 | \([1, -1, 0, -146470, 17486496]\) | \(611960049/122500\) | \(69563983375022500\) | \([2, 2]\) | \(737280\) | \(1.9478\) | |
| 82810.q4 | 82810e1 | \([1, -1, 0, 19150, 1620100]\) | \(1367631/2800\) | \(-1590033905714800\) | \([2]\) | \(368640\) | \(1.6013\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 82810.q have rank \(0\).
Complex multiplication
The elliptic curves in class 82810.q do not have complex multiplication.Modular form 82810.2.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.
