# Properties

 Label 7350.cf Number of curves $2$ Conductor $7350$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cf1")

sage: E.isogeny_class()

## Elliptic curves in class 7350.cf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.cf1 7350bx1 $$[1, 1, 1, -1308938, 328171031]$$ $$393349474783/153600000$$ $$96848656800000000000$$ $$$$ $$376320$$ $$2.5337$$ $$\Gamma_0(N)$$-optimal
7350.cf2 7350bx2 $$[1, 1, 1, 4179062, 2369707031]$$ $$12801408679457/11250000000$$ $$-7093407480468750000000$$ $$$$ $$752640$$ $$2.8803$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7350.2.a.cf

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 