# Properties

 Label 2394.h Number of curves $4$ Conductor $2394$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 2394.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.h1 2394k3 $$[1, -1, 1, -56516, -5157169]$$ $$27384399945278713/153257496$$ $$111724714584$$ $$[2]$$ $$6144$$ $$1.3122$$
2394.h2 2394k2 $$[1, -1, 1, -3596, -76849]$$ $$7052482298233/499254336$$ $$363956410944$$ $$[2, 2]$$ $$3072$$ $$0.96561$$
2394.h3 2394k1 $$[1, -1, 1, -716, 6095]$$ $$55611739513/11440128$$ $$8339853312$$ $$[4]$$ $$1536$$ $$0.61903$$ $$\Gamma_0(N)$$-optimal
2394.h4 2394k4 $$[1, -1, 1, 3244, -339505]$$ $$5180411077127/70976229912$$ $$-51741671605848$$ $$[2]$$ $$6144$$ $$1.3122$$

## Rank

sage: E.rank()

The elliptic curves in class 2394.h have rank $$1$$.

## Complex multiplication

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

## Modular form2394.2.a.h

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.