Properties

 Label 7098.f Number of curves $6$ Conductor $7098$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

Elliptic curves in class 7098.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7098.f1 7098b4 [1, 1, 0, -227139, 41571873] [2] 30720
7098.f2 7098b5 [1, 1, 0, -154469, -23207517] [2] 61440
7098.f3 7098b3 [1, 1, 0, -17579, 310185] [2, 2] 30720
7098.f4 7098b2 [1, 1, 0, -14199, 644805] [2, 2] 15360
7098.f5 7098b1 [1, 1, 0, -679, 14773] [2] 7680 $$\Gamma_0(N)$$-optimal
7098.f6 7098b6 [1, 1, 0, 65231, 2479807] [2] 61440

Rank

sage: E.rank()

The elliptic curves in class 7098.f have rank $$0$$.

Complex multiplication

The elliptic curves in class 7098.f do not have complex multiplication.

Modular form7098.2.a.f

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + 2q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - 2q^{10} + 4q^{11} - q^{12} - q^{14} - 2q^{15} + q^{16} + 2q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.