Properties

 Label 4200.j Number of curves $2$ Conductor $4200$ CM no Rank $1$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

Elliptic curves in class 4200.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4200.j1 4200h1 $$[0, -1, 0, -28, 52]$$ $$78608/21$$ $$672000$$ $$$$ $$512$$ $$-0.17350$$ $$\Gamma_0(N)$$-optimal
4200.j2 4200h2 $$[0, -1, 0, 72, 252]$$ $$318028/441$$ $$-56448000$$ $$$$ $$1024$$ $$0.17307$$

Rank

sage: E.rank()

The elliptic curves in class 4200.j have rank $$1$$.

Complex multiplication

The elliptic curves in class 4200.j do not have complex multiplication.

Modular form4200.2.a.j

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} + 2 q^{11} - 2 q^{13} - 6 q^{19} + O(q^{20})$$ 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 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. 