# Properties

 Label 7350.bh Number of curves $2$ Conductor $7350$ CM no Rank $1$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 7350.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.bh1 7350z1 $$[1, 0, 1, -376, -1102]$$ $$1092727/540$$ $$2894062500$$ $$$$ $$4608$$ $$0.50859$$ $$\Gamma_0(N)$$-optimal
7350.bh2 7350z2 $$[1, 0, 1, 1374, -8102]$$ $$53582633/36450$$ $$-195349218750$$ $$$$ $$9216$$ $$0.85516$$

## Rank

sage: E.rank()

The elliptic curves in class 7350.bh have rank $$1$$.

## Complex multiplication

The elliptic curves in class 7350.bh do not have complex multiplication.

## Modular form7350.2.a.bh

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 2q^{11} + q^{12} - 2q^{13} + q^{16} + 4q^{17} - q^{18} + O(q^{20})$$ ## 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. 