Properties

 Label 450800l Number of curves $2$ Conductor $450800$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

Elliptic curves in class 450800l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450800.l2 450800l1 $$[0, 1, 0, 675792, 1006069588]$$ $$4533086375/60669952$$ $$-456816587702272000000$$ $$[2]$$ $$18579456$$ $$2.6450$$ $$\Gamma_0(N)$$-optimal*
450800.l1 450800l2 $$[0, 1, 0, -11868208, 14729205588]$$ $$24553362849625/1755162752$$ $$13215561127043072000000$$ $$[2]$$ $$37158912$$ $$2.9916$$ $$\Gamma_0(N)$$-optimal*
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 450800l1.

Rank

sage: E.rank()

The elliptic curves in class 450800l have rank $$1$$.

Complex multiplication

The elliptic curves in class 450800l do not have complex multiplication.

Modular form 450800.2.a.l

sage: E.q_eigenform(10)

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

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 Cremona 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 Cremona labels.