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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 388416.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 388416.u1 | 388416u3 | \([0, -1, 0, -146377729, 588577138273]\) | \(438536015880092936/64602489661101\) | \(51096684192288342129672192\) | \([2]\) | \(84934656\) | \(3.6577\) | |
| 388416.u2 | 388416u2 | \([0, -1, 0, -39320569, -85818735431]\) | \(68003243639904448/7163272192041\) | \(708214688977595958595584\) | \([2, 2]\) | \(42467328\) | \(3.3112\) | |
| 388416.u3 | 388416u1 | \([0, -1, 0, -38267164, -91100718782]\) | \(4011705594213827392/52680152007\) | \(81380531455964862912\) | \([2]\) | \(21233664\) | \(2.9646\) | \(\Gamma_0(N)\)-optimal |
| 388416.u4 | 388416u4 | \([0, -1, 0, 50882111, -422184529151]\) | \(18419405270942584/108003564029403\) | \(-85424323920056580220747776\) | \([2]\) | \(84934656\) | \(3.6577\) |
Rank
sage: E.rank()
The elliptic curves in class 388416.u have rank \(0\).
Complex multiplication
The elliptic curves in class 388416.u do not have complex multiplication.Modular form 388416.2.a.u
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.
