# Properties

 Label 37440.eh Number of curves $6$ Conductor $37440$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("37440.eh1")

sage: E.isogeny_class()

## Elliptic curves in class 37440.eh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37440.eh1 37440ey6 [0, 0, 0, -5192652, -4554407536] [2] 786432
37440.eh2 37440ey4 [0, 0, 0, -486732, 130599056] [2] 393216
37440.eh3 37440ey3 [0, 0, 0, -325452, -70742896] [2, 2] 393216
37440.eh4 37440ey5 [0, 0, 0, -66252, -180332656] [2] 786432
37440.eh5 37440ey2 [0, 0, 0, -37452, 1026704] [2, 2] 196608
37440.eh6 37440ey1 [0, 0, 0, 8628, 123536] [2] 98304 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 37440.eh have rank $$0$$.

## Modular form 37440.2.a.eh

sage: E.q_eigenform(10)

$$q + q^{5} - 4q^{11} - q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.