# Properties

 Label 2394.c Number of curves $4$ Conductor $2394$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 2394.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2394.c1 2394b3 $$[1, -1, 0, -152187, 16325477]$$ $$19804628171203875/5638671302656$$ $$110985967250178048$$ $$$$ $$27648$$ $$1.9774$$
2394.c2 2394b1 $$[1, -1, 0, -139692, 20130768]$$ $$11165451838341046875/572244736$$ $$15450607872$$ $$$$ $$9216$$ $$1.4280$$ $$\Gamma_0(N)$$-optimal
2394.c3 2394b2 $$[1, -1, 0, -139452, 20203200]$$ $$-11108001800138902875/79947274872976$$ $$-2158576421570352$$ $$$$ $$18432$$ $$1.7746$$
2394.c4 2394b4 $$[1, -1, 0, 400773, 107342693]$$ $$361682234074684125/462672528510976$$ $$-9106783378681540608$$ $$$$ $$55296$$ $$2.3239$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form2394.2.a.c

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 