Properties

 Label 15680.co Number of curves $2$ Conductor $15680$ CM no Rank $0$ Graph

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Show commands for: SageMath
sage: E = EllipticCurve("co1")

sage: E.isogeny_class()

Elliptic curves in class 15680.co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.co1 15680m2 $$[0, 1, 0, -2081, 38975]$$ $$-77626969/8000$$ $$-102760448000$$ $$[]$$ $$13824$$ $$0.85243$$
15680.co2 15680m1 $$[0, 1, 0, 159, -1]$$ $$34391/20$$ $$-256901120$$ $$[]$$ $$4608$$ $$0.30313$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 15680.co have rank $$0$$.

Complex multiplication

The elliptic curves in class 15680.co do not have complex multiplication.

Modular form 15680.2.a.co

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 2q^{9} + 6q^{11} - 4q^{13} - q^{15} + 2q^{19} + O(q^{20})$$

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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with LMFDB labels.