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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 5520.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5520.q1 | 5520e3 | \([0, 1, 0, -2456, -47676]\) | \(1600610497636/9315\) | \(9538560\) | \([2]\) | \(3584\) | \(0.52925\) | |
| 5520.q2 | 5520e2 | \([0, 1, 0, -156, -756]\) | \(1650587344/119025\) | \(30470400\) | \([2, 2]\) | \(1792\) | \(0.18267\) | |
| 5520.q3 | 5520e1 | \([0, 1, 0, -31, 44]\) | \(212629504/43125\) | \(690000\) | \([2]\) | \(896\) | \(-0.16390\) | \(\Gamma_0(N)\)-optimal |
| 5520.q4 | 5520e4 | \([0, 1, 0, 144, -3036]\) | \(320251964/4197615\) | \(-4298357760\) | \([2]\) | \(3584\) | \(0.52925\) |
Rank
sage: E.rank()
The elliptic curves in class 5520.q have rank \(0\).
Complex multiplication
The elliptic curves in class 5520.q do not have complex multiplication.Modular form 5520.2.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.
