# Properties

 Label 35280.bl Number of curves $4$ Conductor $35280$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35280.bl1")

sage: E.isogeny_class()

## Elliptic curves in class 35280.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35280.bl1 35280cv3 [0, 0, 0, -742203, -245805462] [2] 331776
35280.bl2 35280cv4 [0, 0, 0, -530523, -388943478] [2] 663552
35280.bl3 35280cv1 [0, 0, 0, -36603, 2361898] [2] 110592 $$\Gamma_0(N)$$-optimal
35280.bl4 35280cv2 [0, 0, 0, 57477, 12503722] [2] 221184

## Rank

sage: E.rank()

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

## Modular form 35280.2.a.bl

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.