Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 3850.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3850.j1 | 3850c4 | \([1, 1, 0, -88000, -10029750]\) | \(4823468134087681/30382271150\) | \(474722986718750\) | \([2]\) | \(27648\) | \(1.6535\) | |
3850.j2 | 3850c2 | \([1, 1, 0, -6750, 201500]\) | \(2177286259681/105875000\) | \(1654296875000\) | \([2]\) | \(9216\) | \(1.1042\) | |
3850.j3 | 3850c3 | \([1, 1, 0, -2250, -340000]\) | \(-80677568161/3131816380\) | \(-48934630937500\) | \([2]\) | \(13824\) | \(1.3070\) | |
3850.j4 | 3850c1 | \([1, 1, 0, 250, 12500]\) | \(109902239/4312000\) | \(-67375000000\) | \([2]\) | \(4608\) | \(0.75766\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3850.j have rank \(1\).
Complex multiplication
The elliptic curves in class 3850.j do not have complex multiplication.Modular form 3850.2.a.j
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.