Properties

 Label 1960k Number of curves $2$ Conductor $1960$ CM no Rank $1$ Graph Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 1960k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1960.b2 1960k1 $$[0, 1, 0, 1944, -35456]$$ $$19652/25$$ $$-1033052339200$$ $$$$ $$2688$$ $$0.99128$$ $$\Gamma_0(N)$$-optimal
1960.b1 1960k2 $$[0, 1, 0, -11776, -353760]$$ $$2185454/625$$ $$51652616960000$$ $$$$ $$5376$$ $$1.3379$$

Rank

sage: E.rank()

The elliptic curves in class 1960k have rank $$1$$.

Complex multiplication

The elliptic curves in class 1960k do not have complex multiplication.

Modular form1960.2.a.k

sage: E.q_eigenform(10)

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