# Properties

 Label 2400.j Number of curves $4$ Conductor $2400$ CM no Rank $0$ Graph # Learn more

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

sage: E.isogeny_class()

## Elliptic curves in class 2400.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.j1 2400r3 $$[0, -1, 0, -2033, 35937]$$ $$14526784/15$$ $$960000000$$ $$$$ $$1536$$ $$0.64145$$
2400.j2 2400r2 $$[0, -1, 0, -1408, -19688]$$ $$38614472/405$$ $$3240000000$$ $$$$ $$1536$$ $$0.64145$$
2400.j3 2400r1 $$[0, -1, 0, -158, 312]$$ $$438976/225$$ $$225000000$$ $$[2, 2]$$ $$768$$ $$0.29488$$ $$\Gamma_0(N)$$-optimal
2400.j4 2400r4 $$[0, -1, 0, 592, 1812]$$ $$2863288/1875$$ $$-15000000000$$ $$$$ $$1536$$ $$0.64145$$

## Rank

sage: E.rank()

The elliptic curves in class 2400.j have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2400.j do not have complex multiplication.

## Modular form2400.2.a.j

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + 4q^{11} - 2q^{13} + 2q^{17} + 8q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 