# Properties

 Label 35574bg Number of curves $6$ Conductor $35574$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35574.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 35574bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35574.bj5 35574bg1 [1, 0, 1, -23840, 3126638] [2] 245760 $$\Gamma_0(N)$$-optimal
35574.bj4 35574bg2 [1, 0, 1, -498160, 135177326] [2, 2] 491520
35574.bj3 35574bg3 [1, 0, 1, -616740, 65926606] [2, 2] 983040
35574.bj1 35574bg4 [1, 0, 1, -7968700, 8657569358] [2] 983040
35574.bj6 35574bg5 [1, 0, 1, 2288470, 509842694] [2] 1966080
35574.bj2 35574bg6 [1, 0, 1, -5419230, -4809561242] [2] 1966080

## Rank

sage: E.rank()

The elliptic curves in class 35574bg have rank $$0$$.

## Modular form 35574.2.a.bj

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + 2q^{5} - q^{6} - q^{8} + q^{9} - 2q^{10} + q^{12} + 6q^{13} + 2q^{15} + q^{16} + 2q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.