Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 46800.d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46800.d1 | 46800do3 | \([0, 0, 0, -747075, -238562750]\) | \(988345570681/44994560\) | \(2099266191360000000\) | \([2]\) | \(995328\) | \(2.2776\) | |
| 46800.d2 | 46800do1 | \([0, 0, 0, -117075, 15327250]\) | \(3803721481/26000\) | \(1213056000000000\) | \([2]\) | \(331776\) | \(1.7283\) | \(\Gamma_0(N)\)-optimal |
| 46800.d3 | 46800do2 | \([0, 0, 0, -45075, 33975250]\) | \(-217081801/10562500\) | \(-492804000000000000\) | \([2]\) | \(663552\) | \(2.0749\) | |
| 46800.d4 | 46800do4 | \([0, 0, 0, 404925, -907874750]\) | \(157376536199/7722894400\) | \(-360319361126400000000\) | \([2]\) | \(1990656\) | \(2.6242\) |
Rank
sage: E.rank()
The elliptic curves in class 46800.d have rank \(1\).
Complex multiplication
The elliptic curves in class 46800.d do not have complex multiplication.Modular form 46800.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
