# Properties

 Label 3696w Number of curves 6 Conductor 3696 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("3696.t1")

sage: E.isogeny_class()

## Elliptic curves in class 3696w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3696.t4 3696w1 [0, 1, 0, -544, -5068] [2] 1280 $$\Gamma_0(N)$$-optimal
3696.t3 3696w2 [0, 1, 0, -624, -3564] [2, 2] 2560
3696.t2 3696w3 [0, 1, 0, -4544, 114036] [2, 4] 5120
3696.t6 3696w4 [0, 1, 0, 2016, -23628] [2] 5120
3696.t1 3696w5 [0, 1, 0, -72304, 7459220] [4] 10240
3696.t5 3696w6 [0, 1, 0, 496, 357972] [4] 10240

## Rank

sage: E.rank()

The elliptic curves in class 3696w have rank $$0$$.

## Modular form3696.2.a.t

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} - q^{7} + q^{9} + q^{11} + 6q^{13} - 2q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.