Properties

 Label 239343.f Number of curves $6$ Conductor $239343$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("239343.f1")

sage: E.isogeny_class()

Elliptic curves in class 239343.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
239343.f1 239343f5 [1, 0, 1, -7282822, 7563031751] [2] 7077888
239343.f2 239343f3 [1, 0, 1, -501437, 92658035] [2, 2] 3538944
239343.f3 239343f2 [1, 0, 1, -196392, -32410415] [2, 2] 1769472
239343.f4 239343f1 [1, 0, 1, -194587, -33054439] [2] 884736 $$\Gamma_0(N)$$-optimal
239343.f5 239343f4 [1, 0, 1, 79773, -116254109] [2] 3538944
239343.f6 239343f6 [1, 0, 1, 1399228, 627885299] [2] 7077888

Rank

sage: E.rank()

The elliptic curves in class 239343.f have rank $$0$$.

Modular form 239343.2.a.f

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} - 3q^{8} + q^{9} - 2q^{10} + 4q^{11} - q^{12} - q^{13} - 2q^{15} - q^{16} + q^{17} + q^{18} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.