Properties

 Label 1320.k Number of curves $2$ Conductor $1320$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 1320.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1320.k1 1320d2 $$[0, 1, 0, -1716, 17424]$$ $$2184181167184/717482205$$ $$183675444480$$ $$$$ $$1536$$ $$0.86438$$
1320.k2 1320d1 $$[0, 1, 0, 309, 2034]$$ $$203269830656/218317275$$ $$-3493076400$$ $$$$ $$768$$ $$0.51781$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 1320.k have rank $$1$$.

Complex multiplication

The elliptic curves in class 1320.k do not have complex multiplication.

Modular form1320.2.a.k

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 2 q^{7} + q^{9} + q^{11} - q^{15} - 8 q^{17} - 8 q^{19} + O(q^{20})$$ 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels. 