Properties

 Label 117600.k Number of curves $4$ Conductor $117600$ CM no Rank $0$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

Elliptic curves in class 117600.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
117600.k1 117600bc4 $$[0, -1, 0, -125023500408, -17015100987713688]$$ $$229625675762164624948320008/9568125$$ $$9005442705000000000$$ $$[2]$$ $$247726080$$ $$4.5377$$
117600.k2 117600bc3 $$[0, -1, 0, -7840766033, -263943665448063]$$ $$7079962908642659949376/100085966990454375$$ $$753600891549437872920000000000$$ $$[2]$$ $$247726080$$ $$4.5377$$
117600.k3 117600bc1 $$[0, -1, 0, -7813969158, -265858972088688]$$ $$448487713888272974160064/91549016015625$$ $$10770650185222265625000000$$ $$[2, 2]$$ $$123863040$$ $$4.1911$$ $$\Gamma_0(N)$$-optimal
117600.k4 117600bc2 $$[0, -1, 0, -7787178408, -267772528198188]$$ $$-55486311952875723077768/801237030029296875$$ $$-754117882767333984375000000000$$ $$[2]$$ $$247726080$$ $$4.5377$$

Rank

sage: E.rank()

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

Complex multiplication

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

Modular form 117600.2.a.k

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.