# Properties

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

Show commands: SageMath
E = EllipticCurve("h1")

E.isogeny_class()

## Elliptic curves in class 3192.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3192.h1 3192j3 $$[0, -1, 0, -3232, -57620]$$ $$1823652903746/328593657$$ $$672959809536$$ $$$$ $$5120$$ $$0.98860$$
3192.h2 3192j2 $$[0, -1, 0, -952, 10780]$$ $$93280467172/7800849$$ $$7988069376$$ $$[2, 2]$$ $$2560$$ $$0.64202$$
3192.h3 3192j1 $$[0, -1, 0, -932, 11268]$$ $$350104249168/2793$$ $$715008$$ $$$$ $$1280$$ $$0.29545$$ $$\Gamma_0(N)$$-optimal
3192.h4 3192j4 $$[0, -1, 0, 1008, 47628]$$ $$55251546334/517244049$$ $$-1059315812352$$ $$$$ $$5120$$ $$0.98860$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3192.2.a.h

sage: E.q_eigenform(10)

$$q - q^{3} + 2 q^{5} - q^{7} + q^{9} - 4 q^{11} - 6 q^{13} - 2 q^{15} + 2 q^{17} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 