Show commands:
SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 46200p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46200.bi4 | 46200p1 | \([0, -1, 0, 692, -277388]\) | \(9148592/8301447\) | \(-33205788000000\) | \([2]\) | \(131072\) | \(1.2735\) | \(\Gamma_0(N)\)-optimal |
| 46200.bi3 | 46200p2 | \([0, -1, 0, -59808, -5480388]\) | \(1478729816932/38900169\) | \(622402704000000\) | \([2, 2]\) | \(262144\) | \(1.6201\) | |
| 46200.bi2 | 46200p3 | \([0, -1, 0, -136808, 11613612]\) | \(8849350367426/3314597517\) | \(106067120544000000\) | \([2]\) | \(524288\) | \(1.9666\) | |
| 46200.bi1 | 46200p4 | \([0, -1, 0, -950808, -356534388]\) | \(2970658109581346/2139291\) | \(68457312000000\) | \([2]\) | \(524288\) | \(1.9666\) |
Rank
sage: E.rank()
The elliptic curves in class 46200p have rank \(1\).
Complex multiplication
The elliptic curves in class 46200p do not have complex multiplication.Modular form 46200.2.a.p
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.
