# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("7350.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 7350.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.bb1 7350be2 [1, 0, 1, -279326, -56844952] [] 38880
7350.bb2 7350be1 [1, 0, 1, -3701, -66202]  12960 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form7350.2.a.bb

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + q^{12} - 4q^{13} + q^{16} + 3q^{17} - q^{18} + 2q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 