# Properties

 Label 37180d Number of curves $4$ Conductor $37180$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 37180d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37180.a4 37180d1 [0, 1, 0, -7661, 250264]  77760 $$\Gamma_0(N)$$-optimal
37180.a3 37180d2 [0, 1, 0, -16956, -485900]  155520
37180.a2 37180d3 [0, 1, 0, -75261, -7871876]  233280
37180.a1 37180d4 [0, 1, 0, -1199956, -506336700]  466560

## Rank

sage: E.rank()

The elliptic curves in class 37180d have rank $$1$$.

## Complex multiplication

The elliptic curves in class 37180d do not have complex multiplication.

## Modular form 37180.2.a.d

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 