# Properties

 Label 65366.t Number of curves $2$ Conductor $65366$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 65366.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
65366.t1 65366r2 $$[1, 1, 1, -18033, 13523]$$ $$5512402554625/3188422748$$ $$375114747879452$$ $$$$ $$258048$$ $$1.4860$$
65366.t2 65366r1 $$[1, 1, 1, 4507, 4507]$$ $$86058173375/49827568$$ $$-5862163547632$$ $$$$ $$129024$$ $$1.1394$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 65366.t have rank $$0$$.

## Complex multiplication

The elliptic curves in class 65366.t do not have complex multiplication.

## Modular form 65366.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{8} + q^{9} + 4q^{11} + 2q^{12} + 2q^{13} + q^{16} - 4q^{17} + q^{18} + O(q^{20})$$ ## 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. 