Properties

 Label 8280.n Number of curves $2$ Conductor $8280$ CM no Rank $1$ Graph

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Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

Elliptic curves in class 8280.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8280.n1 8280q2 $$[0, 0, 0, -1347, 18414]$$ $$9776035692/359375$$ $$9936000000$$ $$[2]$$ $$4608$$ $$0.68765$$
8280.n2 8280q1 $$[0, 0, 0, 33, 1026]$$ $$574992/66125$$ $$-457056000$$ $$[2]$$ $$2304$$ $$0.34107$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 8280.n have rank $$1$$.

Complex multiplication

The elliptic curves in class 8280.n do not have complex multiplication.

Modular form8280.2.a.n

sage: E.q_eigenform(10)

$$q + q^{5} - 2 q^{7} - 2 q^{13} + 6 q^{17} + O(q^{20})$$

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.