Properties

 Label 46800fq Number of curves $2$ Conductor $46800$ CM no Rank $1$ Graph

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Show commands: SageMath
sage: E = EllipticCurve("fq1")

sage: E.isogeny_class()

Elliptic curves in class 46800fq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.o2 46800fq1 $$[0, 0, 0, -1281315, -558249950]$$ $$623295446073461/5458752$$ $$2037468266496000$$ $$[2]$$ $$589824$$ $$2.1044$$ $$\Gamma_0(N)$$-optimal
46800.o1 46800fq2 $$[0, 0, 0, -1310115, -531840350]$$ $$666276475992821/58199166792$$ $$21722722606780416000$$ $$[2]$$ $$1179648$$ $$2.4510$$

Rank

sage: E.rank()

The elliptic curves in class 46800fq have rank $$1$$.

Complex multiplication

The elliptic curves in class 46800fq do not have complex multiplication.

Modular form 46800.2.a.fq

sage: E.q_eigenform(10)

$$q - 4q^{7} + 2q^{11} + q^{13} - 4q^{17} - 2q^{19} + O(q^{20})$$

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.