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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 5184.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5184.q1 | 5184p3 | \([0, 0, 0, -68940, 6967152]\) | \(-189613868625/128\) | \(-24461180928\) | \([]\) | \(8064\) | \(1.3091\) | |
| 5184.q2 | 5184p4 | \([0, 0, 0, -54540, 9958896]\) | \(-1159088625/2097152\) | \(-32462531054272512\) | \([]\) | \(24192\) | \(1.8584\) | |
| 5184.q3 | 5184p2 | \([0, 0, 0, -2700, -56592]\) | \(-140625/8\) | \(-123834728448\) | \([]\) | \(3456\) | \(0.88544\) | |
| 5184.q4 | 5184p1 | \([0, 0, 0, 180, -144]\) | \(3375/2\) | \(-382205952\) | \([]\) | \(1152\) | \(0.33613\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5184.q have rank \(0\).
Complex multiplication
The elliptic curves in class 5184.q do not have complex multiplication.Modular form 5184.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
