Properties

 Label 32340k Number of curves $2$ Conductor $32340$ CM no Rank $0$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 32340k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.l2 32340k1 $$[0, -1, 0, -4033745, 4282003650]$$ $$-3856034557002072064/1973796785296875$$ $$-3715443487894272750000$$ $$$$ $$1935360$$ $$2.8436$$ $$\Gamma_0(N)$$-optimal
32340.l1 32340k2 $$[0, -1, 0, -71010620, 230315561400]$$ $$1314817350433665559504/190690249278375$$ $$5743236387161994336000$$ $$$$ $$3870720$$ $$3.1901$$

Rank

sage: E.rank()

The elliptic curves in class 32340k have rank $$0$$.

Complex multiplication

The elliptic curves in class 32340k do not have complex multiplication.

Modular form 32340.2.a.k

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} - q^{11} - q^{15} + 2 q^{17} + 6 q^{19} + O(q^{20})$$ 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 Cremona 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 Cremona labels. 