Properties

 Label 46200dd Number of curves $2$ Conductor $46200$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("dd1")

sage: E.isogeny_class()

Elliptic curves in class 46200dd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46200.cp2 46200dd1 $$[0, 1, 0, -148, 608]$$ $$11279504/693$$ $$22176000$$ $$$$ $$9216$$ $$0.16142$$ $$\Gamma_0(N)$$-optimal
46200.cp1 46200dd2 $$[0, 1, 0, -448, -2992]$$ $$77860436/17787$$ $$2276736000$$ $$$$ $$18432$$ $$0.50799$$

Rank

sage: E.rank()

The elliptic curves in class 46200dd have rank $$1$$.

Complex multiplication

The elliptic curves in class 46200dd do not have complex multiplication.

Modular form 46200.2.a.dd

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} + q^{11} + 4 q^{13} - 2 q^{17} + 4 q^{19} + O(q^{20})$$ 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. 