Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 397800.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
397800.d1 | 397800d1 | \([0, 0, 0, -95475, 11074750]\) | \(8251733668/232713\) | \(2714364432000000\) | \([2]\) | \(3670016\) | \(1.7403\) | \(\Gamma_0(N)\)-optimal |
397800.d2 | 397800d2 | \([0, 0, 0, 21525, 36463750]\) | \(47279806/24649677\) | \(-575027665056000000\) | \([2]\) | \(7340032\) | \(2.0868\) |
Rank
sage: E.rank()
The elliptic curves in class 397800.d have rank \(0\).
Complex multiplication
The elliptic curves in class 397800.d do not have complex multiplication.Modular form 397800.2.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.