# Properties

 Label 3192.c Number of curves $4$ Conductor $3192$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("c1")

E.isogeny_class()

## Elliptic curves in class 3192.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.c1 3192b3 $$[0, -1, 0, -20104, -1089956]$$ $$877592260337188/494771571$$ $$506646088704$$ $$$$ $$6144$$ $$1.1928$$
3192.c2 3192b4 $$[0, -1, 0, -11744, 486588]$$ $$174947951977348/2957342913$$ $$3028319142912$$ $$$$ $$6144$$ $$1.1928$$
3192.c3 3192b2 $$[0, -1, 0, -1484, -9996]$$ $$1412791482832/631868769$$ $$161758404864$$ $$[2, 2]$$ $$3072$$ $$0.84622$$
3192.c4 3192b1 $$[0, -1, 0, 321, -1332]$$ $$227910944768/172414683$$ $$-2758634928$$ $$$$ $$1536$$ $$0.49965$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3192.c have rank $$0$$.

## Complex multiplication

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

## Modular form3192.2.a.c

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 