# Properties

 Label 36414t Number of curves $6$ Conductor $36414$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("36414.j1")

sage: E.isogeny_class()

## Elliptic curves in class 36414t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
36414.j5 36414t1 [1, -1, 0, -182704698, -949310141004] [2] 8847360 $$\Gamma_0(N)$$-optimal
36414.j4 36414t2 [1, -1, 0, -235973178, -350583079500] [2, 2] 17694720
36414.j6 36414t3 [1, -1, 0, 910131462, -2758090486284] [2] 35389440
36414.j2 36414t4 [1, -1, 0, -2234373498, 40374817041780] [2, 2] 35389440
36414.j3 36414t5 [1, -1, 0, -761063058, 92822606071164] [2] 70778880
36414.j1 36414t6 [1, -1, 0, -35682089058, 2594328654970476] [2] 70778880

## Rank

sage: E.rank()

The elliptic curves in class 36414t have rank $$0$$.

## Modular form 36414.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - 2q^{5} - q^{7} - q^{8} + 2q^{10} + 4q^{11} - 2q^{13} + q^{14} + q^{16} + 4q^{19} + O(q^{20})$$

## 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.