Properties

 Label 262080e Number of curves 2 Conductor 262080 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("262080.e1")

sage: E.isogeny_class()

Elliptic curves in class 262080e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.e1 262080e1 [0, 0, 0, -19525068, -30560756112] [2] 32440320 $$\Gamma_0(N)$$-optimal
262080.e2 262080e2 [0, 0, 0, 21762612, -142582489488] [2] 64880640

Rank

sage: E.rank()

The elliptic curves in class 262080e have rank $$0$$.

Modular form 262080.2.a.e

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 6q^{11} - q^{13} + 8q^{17} + O(q^{20})$$

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 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.