Properties

 Label 35280cq Number of curves $6$ Conductor $35280$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.dm1")

sage: E.isogeny_class()

Elliptic curves in class 35280cq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.dm4 35280cq1 [0, 0, 0, -77322, -8275561] [2] 98304 $$\Gamma_0(N)$$-optimal
35280.dm3 35280cq2 [0, 0, 0, -79527, -7778554] [2, 2] 196608
35280.dm5 35280cq3 [0, 0, 0, 105693, -38636206] [4] 393216
35280.dm2 35280cq4 [0, 0, 0, -300027, 54887546] [2, 2] 393216
35280.dm6 35280cq5 [0, 0, 0, 493773, 296043986] [2] 786432
35280.dm1 35280cq6 [0, 0, 0, -4621827, 3824361506] [2] 786432

Rank

sage: E.rank()

The elliptic curves in class 35280cq have rank $$0$$.

Modular form 35280.2.a.dm

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.