Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 4641.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4641.d1 | 4641g1 | \([1, 0, 0, -455, 3696]\) | \(10418796526321/6390657\) | \(6390657\) | \([2]\) | \(2240\) | \(0.24865\) | \(\Gamma_0(N)\)-optimal |
4641.d2 | 4641g2 | \([1, 0, 0, -370, 5141]\) | \(-5602762882081/8312741073\) | \(-8312741073\) | \([2]\) | \(4480\) | \(0.59522\) |
Rank
sage: E.rank()
The elliptic curves in class 4641.d have rank \(1\).
Complex multiplication
The elliptic curves in class 4641.d do not have complex multiplication.Modular form 4641.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.