Properties

 Label 35280fr Number of curves 8 Conductor 35280 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.do1")

sage: E.isogeny_class()

Elliptic curves in class 35280fr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.do7 35280fr1 [0, 0, 0, -147, -110446] [2] 49152 $$\Gamma_0(N)$$-optimal
35280.do6 35280fr2 [0, 0, 0, -35427, -2530654] [2, 2] 98304
35280.do5 35280fr3 [0, 0, 0, -70707, 3346994] [2, 2] 196608
35280.do4 35280fr4 [0, 0, 0, -564627, -163301614] [2] 196608
35280.do8 35280fr5 [0, 0, 0, 246813, 25128866] [2] 393216
35280.do2 35280fr6 [0, 0, 0, -952707, 357734594] [2, 2] 393216
35280.do3 35280fr7 [0, 0, 0, -776307, 494303474] [2] 786432
35280.do1 35280fr8 [0, 0, 0, -15241107, 22901972114] [2] 786432

Rank

sage: E.rank()

The elliptic curves in class 35280fr have rank $$1$$.

Modular form 35280.2.a.do

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.