Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 163170.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
163170.u1 | 163170en2 | \([1, -1, 0, -10454355, 13010350261]\) | \(1473328864410526369/362154602880\) | \(31060595491313028480\) | \([2]\) | \(6881280\) | \(2.7282\) | |
163170.u2 | 163170en1 | \([1, -1, 0, -575955, 253384501]\) | \(-246362173188769/180452966400\) | \(-15476750951071334400\) | \([2]\) | \(3440640\) | \(2.3816\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 163170.u have rank \(1\).
Complex multiplication
The elliptic curves in class 163170.u do not have complex multiplication.Modular form 163170.2.a.u
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.