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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 46410d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46410.c4 | 46410d1 | \([1, 1, 0, -1533, -5187]\) | \(398834531805529/221870987520\) | \(221870987520\) | \([2]\) | \(73728\) | \(0.86748\) | \(\Gamma_0(N)\)-optimal |
| 46410.c2 | 46410d2 | \([1, 1, 0, -15053, 700557]\) | \(377257581238546009/2489894643600\) | \(2489894643600\) | \([2, 2]\) | \(147456\) | \(1.2141\) | |
| 46410.c3 | 46410d3 | \([1, 1, 0, -5953, 1550497]\) | \(-23337017143411609/1028366161952220\) | \(-1028366161952220\) | \([2]\) | \(294912\) | \(1.5606\) | |
| 46410.c1 | 46410d4 | \([1, 1, 0, -240473, 45288633]\) | \(1537890797739931486489/67654177500\) | \(67654177500\) | \([2]\) | \(294912\) | \(1.5606\) |
Rank
sage: E.rank()
The elliptic curves in class 46410d have rank \(1\).
Complex multiplication
The elliptic curves in class 46410d do not have complex multiplication.Modular form 46410.2.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 Cremona 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 Cremona labels.
