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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 8325q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8325.p3 | 8325q1 | \([0, 0, 1, -750, -7844]\) | \(4096000/37\) | \(421453125\) | \([]\) | \(2880\) | \(0.47749\) | \(\Gamma_0(N)\)-optimal |
| 8325.p2 | 8325q2 | \([0, 0, 1, -5250, 141781]\) | \(1404928000/50653\) | \(576969328125\) | \([]\) | \(8640\) | \(1.0268\) | |
| 8325.p1 | 8325q3 | \([0, 0, 1, -421500, 105328156]\) | \(727057727488000/37\) | \(421453125\) | \([]\) | \(25920\) | \(1.5761\) |
Rank
sage: E.rank()
The elliptic curves in class 8325q have rank \(0\).
Complex multiplication
The elliptic curves in class 8325q do not have complex multiplication.Modular form 8325.2.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 Cremona numbering.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
