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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 1380.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1380.d1 | 1380d3 | \([0, 1, 0, -12165, -520512]\) | \(12444451776495616/912525\) | \(14600400\) | \([2]\) | \(1512\) | \(0.82545\) | |
1380.d2 | 1380d4 | \([0, 1, 0, -12140, -522732]\) | \(-772993034343376/6661615005\) | \(-1705373441280\) | \([2]\) | \(3024\) | \(1.1720\) | |
1380.d3 | 1380d1 | \([0, 1, 0, -165, -612]\) | \(31238127616/9703125\) | \(155250000\) | \([6]\) | \(504\) | \(0.27614\) | \(\Gamma_0(N)\)-optimal |
1380.d4 | 1380d2 | \([0, 1, 0, 460, -3612]\) | \(41957807024/48205125\) | \(-12340512000\) | \([6]\) | \(1008\) | \(0.62271\) |
Rank
sage: E.rank()
The elliptic curves in class 1380.d have rank \(0\).
Complex multiplication
The elliptic curves in class 1380.d do not have complex multiplication.Modular form 1380.2.a.d
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.