Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 270504.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
270504.b1 | 270504b2 | \([0, 0, 0, -2133687, -1199508950]\) | \(238481570896/25857\) | \(116476726699636992\) | \([2]\) | \(4718592\) | \(2.3047\) | |
270504.b2 | 270504b1 | \([0, 0, 0, -143922, -15598775]\) | \(1171019776/304317\) | \(85677592235790672\) | \([2]\) | \(2359296\) | \(1.9582\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 270504.b have rank \(2\).
Complex multiplication
The elliptic curves in class 270504.b do not have complex multiplication.Modular form 270504.2.a.b
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.