Properties

 Label 203280.ee Number of curves $4$ Conductor $203280$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("ee1")

sage: E.isogeny_class()

Elliptic curves in class 203280.ee

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
203280.ee1 203280fv3 $$[0, 1, 0, -3602936, 2630652660]$$ $$1425631925916578/270703125$$ $$982153418400000000$$ $$$$ $$3932160$$ $$2.4535$$
203280.ee2 203280fv4 $$[0, 1, 0, -1579816, -740631916]$$ $$120186986927618/4332064275$$ $$15717409011882547200$$ $$$$ $$3932160$$ $$2.4535$$
203280.ee3 203280fv2 $$[0, 1, 0, -248816, 31880484]$$ $$939083699236/300155625$$ $$544505855160960000$$ $$[2, 2]$$ $$1966080$$ $$2.1069$$
203280.ee4 203280fv1 $$[0, 1, 0, 44004, 3418380]$$ $$20777545136/23059575$$ $$-10457969599123200$$ $$$$ $$983040$$ $$1.7603$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 203280.ee have rank $$1$$.

Complex multiplication

The elliptic curves in class 203280.ee do not have complex multiplication.

Modular form 203280.2.a.ee

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - q^{7} + q^{9} + 2 q^{13} - q^{15} + 2 q^{17} + O(q^{20})$$ 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels. 