# Properties

 Label 1922e Number of curves $2$ Conductor $1922$ CM no Rank $1$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 1922e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1922.c2 1922e1 $$[1, -1, 1, -72, -117]$$ $$42396561/16384$$ $$15745024$$ $$[]$$ $$840$$ $$0.079973$$ $$\Gamma_0(N)$$-optimal
1922.c1 1922e2 $$[1, -1, 1, -76332, 8136267]$$ $$51181724570498001/4$$ $$3844$$ $$[]$$ $$5880$$ $$1.0529$$

## Rank

sage: E.rank()

The elliptic curves in class 1922e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1922e do not have complex multiplication.

## Modular form1922.2.a.e

sage: E.q_eigenform(10)

$$q + q^{2} - 3 q^{3} + q^{4} + q^{5} - 3 q^{6} - 3 q^{7} + q^{8} + 6 q^{9} + q^{10} + 3 q^{11} - 3 q^{12} - 5 q^{13} - 3 q^{14} - 3 q^{15} + q^{16} - 3 q^{17} + 6 q^{18} + 7 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.