# Properties

 Label 19074.j Number of curves 2 Conductor 19074 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19074.j1")

sage: E.isogeny_class()

## Elliptic curves in class 19074.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19074.j1 19074h2 [1, 0, 1, -13738152402, -619785496609820]  27783168
19074.j2 19074h1 [1, 0, 1, -859017682, -9675126653980]  13891584 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 19074.j have rank $$0$$.

## Modular form 19074.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - 2q^{5} - q^{6} + 4q^{7} - q^{8} + q^{9} + 2q^{10} - q^{11} + q^{12} - 4q^{14} - 2q^{15} + q^{16} - q^{18} + 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 