# Properties

 Label 37191i Number of curves 2 Conductor 37191 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("37191.c1")

sage: E.isogeny_class()

## Elliptic curves in class 37191i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37191.c2 37191i1 [1, 0, 0, -1128, 211959] [2] 57600 $$\Gamma_0(N)$$-optimal
37191.c1 37191i2 [1, 0, 0, -60663, 5701086] [2] 115200

## Rank

sage: E.rank()

The elliptic curves in class 37191i have rank $$1$$.

## Modular form 37191.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} - q^{6} + 3q^{8} + q^{9} + q^{11} - q^{12} - 2q^{13} - q^{16} - q^{18} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.