# Properties

 Label 29400.bh Number of curves $2$ Conductor $29400$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

## Elliptic curves in class 29400.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
29400.bh1 29400ba2 [0, -1, 0, -74888, -7849428] [2] 100352
29400.bh2 29400ba1 [0, -1, 0, -6288, -29028] [2] 50176 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 29400.bh have rank $$1$$.

## Complex multiplication

The elliptic curves in class 29400.bh do not have complex multiplication.

## Modular form 29400.2.a.bh

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + 2q^{13} - 6q^{17} - 2q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.