# Properties

 Label 37485.bd Number of curves 4 Conductor 37485 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("37485.bd1")

sage: E.isogeny_class()

## Elliptic curves in class 37485.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
37485.bd1 37485s4 [1, -1, 0, -743535, 246949870]  393216
37485.bd2 37485s3 [1, -1, 0, -236385, -41062820]  393216
37485.bd3 37485s2 [1, -1, 0, -48960, 3431875] [2, 2] 196608
37485.bd4 37485s1 [1, -1, 0, 6165, 311800]  98304 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 37485.bd have rank $$1$$.

## Modular form 37485.2.a.bd

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - q^{5} - 3q^{8} - q^{10} + 6q^{13} - q^{16} - q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 