# Properties

 Label 2400.t Number of curves $2$ Conductor $2400$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 2400.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2400.t1 2400q1 $$[0, 1, 0, -538, 4628]$$ $$2156689088/81$$ $$648000$$ $$$$ $$768$$ $$0.20152$$ $$\Gamma_0(N)$$-optimal
2400.t2 2400q2 $$[0, 1, 0, -513, 5103]$$ $$-29218112/6561$$ $$-3359232000$$ $$$$ $$1536$$ $$0.54809$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2400.2.a.t

sage: E.q_eigenform(10)

$$q + q^{3} - 4 q^{7} + q^{9} + 4 q^{13} - 8 q^{19} + O(q^{20})$$

## 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. 