# Properties

 Label 350.b Number of curves $4$ Conductor $350$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("350.b1")

sage: E.isogeny_class()

## Elliptic curves in class 350.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
350.b1 350a3 [1, -1, 0, -6692, -209034]  384
350.b2 350a4 [1, -1, 0, -2192, 37466]  384
350.b3 350a2 [1, -1, 0, -442, -2784] [2, 2] 192
350.b4 350a1 [1, -1, 0, 58, -284]  96 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 350.b have rank $$0$$.

## Modular form350.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{7} - q^{8} - 3q^{9} + 4q^{11} + 6q^{13} - q^{14} + q^{16} - 2q^{17} + 3q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 