Show commands:
SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 116160f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
116160.q1 | 116160f1 | \([0, -1, 0, -88161, 10100961]\) | \(217190179331/97200\) | \(33914408140800\) | \([2]\) | \(368640\) | \(1.5544\) | \(\Gamma_0(N)\)-optimal |
116160.q2 | 116160f2 | \([0, -1, 0, -74081, 13421025]\) | \(-128864147651/147622500\) | \(-51507507363840000\) | \([2]\) | \(737280\) | \(1.9010\) |
Rank
sage: E.rank()
The elliptic curves in class 116160f have rank \(1\).
Complex multiplication
The elliptic curves in class 116160f do not have complex multiplication.Modular form 116160.2.a.f
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 Cremona 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 Cremona labels.