Properties

 Label 35280.fp Number of curves $6$ Conductor $35280$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.fp1")

sage: E.isogeny_class()

Elliptic curves in class 35280.fp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.fp1 35280fq6 [0, 0, 0, -118540947, 496764671186] [2] 2359296
35280.fp2 35280fq4 [0, 0, 0, -7408947, 7761644786] [2, 2] 1179648
35280.fp3 35280fq5 [0, 0, 0, -6915027, 8841057554] [2] 2359296
35280.fp4 35280fq3 [0, 0, 0, -2610867, -1534719886] [2] 1179648
35280.fp5 35280fq2 [0, 0, 0, -494067, 104106674] [2, 2] 589824
35280.fp6 35280fq1 [0, 0, 0, 70413, 10064306] [2] 294912 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

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

Modular form 35280.2.a.fp

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.