# Properties

 Label 6498.t Number of curves $4$ Conductor $6498$ CM no Rank $0$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 6498.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6498.t1 6498v3 $$[1, -1, 1, -1390640, -630851601]$$ $$8671983378625/82308$$ $$2822871980170692$$ $$$$ $$103680$$ $$2.1270$$
6498.t2 6498v4 $$[1, -1, 1, -1358150, -661756089]$$ $$-8078253774625/846825858$$ $$-29043118367986164642$$ $$$$ $$207360$$ $$2.4736$$
6498.t3 6498v1 $$[1, -1, 1, -26060, 130191]$$ $$57066625/32832$$ $$1126020956079168$$ $$$$ $$34560$$ $$1.5777$$ $$\Gamma_0(N)$$-optimal
6498.t4 6498v2 $$[1, -1, 1, 103900, 961935]$$ $$3616805375/2105352$$ $$-72206093808576648$$ $$$$ $$69120$$ $$1.9243$$

## Rank

sage: E.rank()

The elliptic curves in class 6498.t have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6498.t do not have complex multiplication.

## Modular form6498.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - 4 q^{7} + q^{8} + 4 q^{13} - 4 q^{14} + q^{16} - 6 q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 