Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 54720.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54720.y1 | 54720w2 | \([0, 0, 0, -1151148, 474375472]\) | \(882774443450089/2166000000\) | \(413929046016000000\) | \([2]\) | \(1032192\) | \(2.2585\) | |
54720.y2 | 54720w1 | \([0, 0, 0, -45228, 12985648]\) | \(-53540005609/350208000\) | \(-66925791019008000\) | \([2]\) | \(516096\) | \(1.9120\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54720.y have rank \(0\).
Complex multiplication
The elliptic curves in class 54720.y do not have complex multiplication.Modular form 54720.2.a.y
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.