# Properties

 Label 117600.t Number of curves $4$ Conductor $117600$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 117600.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117600.t1 117600bb4 $$[0, -1, 0, -1372408, 619289812]$$ $$303735479048/105$$ $$98825160000000$$ $$$$ $$1769472$$ $$2.0413$$
117600.t2 117600bb3 $$[0, -1, 0, -178033, -14372063]$$ $$82881856/36015$$ $$271176239040000000$$ $$$$ $$1769472$$ $$2.0413$$
117600.t3 117600bb1 $$[0, -1, 0, -86158, 9607312]$$ $$601211584/11025$$ $$1297080225000000$$ $$[2, 2]$$ $$884736$$ $$1.6947$$ $$\Gamma_0(N)$$-optimal
117600.t4 117600bb2 $$[0, -1, 0, -408, 27786312]$$ $$-8/354375$$ $$-333534915000000000$$ $$$$ $$1769472$$ $$2.0413$$

## Rank

sage: E.rank()

The elliptic curves in class 117600.t have rank $$0$$.

## Complex multiplication

The elliptic curves in class 117600.t do not have complex multiplication.

## Modular form 117600.2.a.t

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} + 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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. 