# Properties

 Label 381150.ev Number of curves 4 Conductor 381150 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("381150.ev1")

sage: E.isogeny_class()

## Elliptic curves in class 381150.ev

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
381150.ev1 381150ev4 [1, -1, 0, -711008667, -7090316624759]  238878720
381150.ev2 381150ev2 [1, -1, 0, -97357167, 366482917741]  79626240
381150.ev3 381150ev1 [1, -1, 0, -1525167, 14108653741]  39813120 $$\Gamma_0(N)$$-optimal
381150.ev4 381150ev3 [1, -1, 0, 13720833, -380046184259]  119439360

## Rank

sage: E.rank()

The elliptic curves in class 381150.ev have rank $$2$$.

## Modular form 381150.2.a.ev

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{7} - q^{8} - 4q^{13} - q^{14} + q^{16} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 