# Properties

 Label 3192.g Number of curves $2$ Conductor $3192$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("g1")

E.isogeny_class()

## Elliptic curves in class 3192.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.g1 3192d2 $$[0, -1, 0, -360088, 83283964]$$ $$5042558062190438500/358269592023$$ $$366868062231552$$ $$$$ $$19200$$ $$1.8469$$
3192.g2 3192d1 $$[0, -1, 0, -23948, 1131348]$$ $$5933482010818000/1304188224633$$ $$333872185506048$$ $$$$ $$9600$$ $$1.5003$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3192.2.a.g

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} + 2 q^{11} - 4 q^{13} + q^{19} + O(q^{20})$$

## 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. 