Properties

 Label 262080p Number of curves 4 Conductor 262080 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("262080.p1")

sage: E.isogeny_class()

Elliptic curves in class 262080p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.p4 262080p1 [0, 0, 0, -278508, -5883568] [2] 3932160 $$\Gamma_0(N)$$-optimal
262080.p2 262080p2 [0, 0, 0, -3227628, -2227160752] [2, 2] 7864320
262080.p3 262080p3 [0, 0, 0, -2029548, -3901118128] [2] 15728640
262080.p1 262080p4 [0, 0, 0, -51611628, -142714943152] [2] 15728640

Rank

sage: E.rank()

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

Modular form 262080.2.a.p

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 4q^{11} + q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.