# Properties

 Label 2394.f Number of curves $2$ Conductor $2394$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 2394.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.f1 2394d2 $$[1, -1, 0, -29295, 1562733]$$ $$3814038123905521/773540010432$$ $$563910667604928$$ $$$$ $$21504$$ $$1.5462$$
2394.f2 2394d1 $$[1, -1, 0, -9135, -312147]$$ $$115650783909361/8339853312$$ $$6079753064448$$ $$$$ $$10752$$ $$1.1997$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2394.f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2394.f do not have complex multiplication.

## Modular form2394.2.a.f

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 4 q^{5} - q^{7} - q^{8} - 4 q^{10} + 6 q^{11} - 4 q^{13} + q^{14} + q^{16} + 4 q^{17} - q^{19} + O(q^{20})$$

## 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. 