# Properties

 Label 394944ev Number of curves $2$ Conductor $394944$ CM no Rank $1$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("ev1")

sage: E.isogeny_class()

## Elliptic curves in class 394944ev

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
394944.ev1 394944ev1 [0, 1, 0, -1517985, -719912481] [2] 8847360 $$\Gamma_0(N)$$-optimal
394944.ev2 394944ev2 [0, 1, 0, -1208225, -1021928481] [2] 17694720

## Rank

sage: E.rank()

The elliptic curves in class 394944ev have rank $$1$$.

## Complex multiplication

The elliptic curves in class 394944ev do not have complex multiplication.

## Modular form 394944.2.a.ev

sage: E.q_eigenform(10)

$$q + q^{3} - 4q^{5} - 2q^{7} + q^{9} - 4q^{15} + q^{17} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.