# Properties

 Label 350.e Number of curves $2$ Conductor $350$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 350.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
350.e1 350b2 $$[1, 0, 0, -1138, -20858]$$ $$-417267265/235298$$ $$-91913281250$$ $$[]$$ $$360$$ $$0.80685$$
350.e2 350b1 $$[1, 0, 0, 112, 392]$$ $$397535/392$$ $$-153125000$$ $$$$ $$120$$ $$0.25755$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 350.e do not have complex multiplication.

## Modular form350.2.a.e

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} - 2q^{9} + 3q^{11} + q^{12} + 2q^{13} + q^{14} + q^{16} + 3q^{17} - 2q^{18} - 7q^{19} + O(q^{20})$$ ## 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. 