Properties

 Label 2880.y Number of curves 8 Conductor 2880 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2880.y1")

sage: E.isogeny_class()

Elliptic curves in class 2880.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.y1 2880r7 [0, 0, 0, -1244172, 534156784] [2] 16384
2880.y2 2880r5 [0, 0, 0, -77772, 8343664] [2, 2] 8192
2880.y3 2880r8 [0, 0, 0, -63372, 11528944] [2] 16384
2880.y4 2880r3 [0, 0, 0, -46092, -3808784] [2] 4096
2880.y5 2880r4 [0, 0, 0, -5772, 78064] [2, 2] 4096
2880.y6 2880r2 [0, 0, 0, -2892, -59024] [2, 2] 2048
2880.y7 2880r1 [0, 0, 0, -12, -2576] [2] 1024 $$\Gamma_0(N)$$-optimal
2880.y8 2880r6 [0, 0, 0, 20148, 586096] [2] 8192

Rank

sage: E.rank()

The elliptic curves in class 2880.y have rank $$1$$.

Modular form2880.2.a.y

sage: E.q_eigenform(10)

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

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 LMFDB numbering.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.