Show commands:
SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 48510.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
48510.d1 | 48510b1 | \([1, -1, 0, -102615, 11723165]\) | \(51603494067/4336640\) | \(10042293356282880\) | \([2]\) | \(368640\) | \(1.8122\) | \(\Gamma_0(N)\)-optimal |
48510.d2 | 48510b2 | \([1, -1, 0, 109065, 53678141]\) | \(61958108493/573927200\) | \(-1329034761370562400\) | \([2]\) | \(737280\) | \(2.1588\) |
Rank
sage: E.rank()
The elliptic curves in class 48510.d have rank \(0\).
Complex multiplication
The elliptic curves in class 48510.d do not have complex multiplication.Modular form 48510.2.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.