# Properties

 Label 3192.a Number of curves $2$ Conductor $3192$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 3192.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.a1 3192m1 $$[0, -1, 0, -106435, -13329764]$$ $$8334147900493981696/232793757$$ $$3724700112$$ $$[2]$$ $$11520$$ $$1.3474$$ $$\Gamma_0(N)$$-optimal
3192.a2 3192m2 $$[0, -1, 0, -106300, -13365404]$$ $$-518904725785387216/2753286252003$$ $$-704841280512768$$ $$[2]$$ $$23040$$ $$1.6940$$

## Rank

sage: E.rank()

The elliptic curves in class 3192.a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3192.a do not have complex multiplication.

## Modular form3192.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - 4 q^{5} - q^{7} + q^{9} - 2 q^{13} + 4 q^{15} + 4 q^{17} + q^{19} + O(q^{20})$$

## 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 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.