# Properties

 Label 381150db Number of curves 4 Conductor 381150 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("381150.db1")

sage: E.isogeny_class()

## Elliptic curves in class 381150db

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
381150.db3 381150db1 [1, -1, 0, -13640292, -16833360384] [2] 35389440 $$\Gamma_0(N)$$-optimal
381150.db2 381150db2 [1, -1, 0, -57744792, 152130979116] [2, 2] 70778880
381150.db1 381150db3 [1, -1, 0, -898180542, 10360904034366] [2] 141557760
381150.db4 381150db4 [1, -1, 0, 77018958, 756546397866] [2] 141557760

## Rank

sage: E.rank()

The elliptic curves in class 381150db have rank $$1$$.

## Modular form 381150.2.a.db

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{7} - q^{8} + 2q^{13} + q^{14} + q^{16} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.