# Properties

 Label 2400.i Number of curves $4$ Conductor $2400$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 2400.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.i1 2400a3 $$[0, -1, 0, -4008, 99012]$$ $$890277128/15$$ $$120000000$$ $$$$ $$1536$$ $$0.68052$$
2400.i2 2400a2 $$[0, -1, 0, -1008, -10488]$$ $$14172488/1875$$ $$15000000000$$ $$$$ $$1536$$ $$0.68052$$
2400.i3 2400a1 $$[0, -1, 0, -258, 1512]$$ $$1906624/225$$ $$225000000$$ $$[2, 2]$$ $$768$$ $$0.33395$$ $$\Gamma_0(N)$$-optimal
2400.i4 2400a4 $$[0, -1, 0, 367, 7137]$$ $$85184/405$$ $$-25920000000$$ $$$$ $$1536$$ $$0.68052$$

## Rank

sage: E.rank()

The elliptic curves in class 2400.i have rank $$1$$.

## Complex multiplication

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

## Modular form2400.2.a.i

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 2 q^{13} - 6 q^{17} + 4 q^{19} + O(q^{20})$$

## 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 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. 