# Properties

 Label 2400.a Number of curves $4$ Conductor $2400$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 2400.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.a1 2400v2 $$[0, -1, 0, -90033, -10368063]$$ $$1261112198464/675$$ $$43200000000$$ $$$$ $$9216$$ $$1.3704$$
2400.a2 2400v3 $$[0, -1, 0, -12408, 300312]$$ $$26410345352/10546875$$ $$84375000000000$$ $$$$ $$9216$$ $$1.3704$$
2400.a3 2400v1 $$[0, -1, 0, -5658, -158688]$$ $$20034997696/455625$$ $$455625000000$$ $$[2, 2]$$ $$4608$$ $$1.0238$$ $$\Gamma_0(N)$$-optimal
2400.a4 2400v4 $$[0, -1, 0, 592, -496188]$$ $$2863288/13286025$$ $$-106288200000000$$ $$$$ $$9216$$ $$1.3704$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2400.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - 4 q^{7} + q^{9} - 4 q^{11} - 6 q^{13} - 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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 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. 