# Properties

 Label 29400.ba Number of curves $2$ Conductor $29400$ CM no Rank $1$ Graph # Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

## Elliptic curves in class 29400.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29400.ba1 29400co1 $$[0, -1, 0, -1283, 13812]$$ $$2725888/675$$ $$57881250000$$ $$$$ $$18432$$ $$0.77547$$ $$\Gamma_0(N)$$-optimal
29400.ba2 29400co2 $$[0, -1, 0, 3092, 83812]$$ $$2382032/3645$$ $$-5000940000000$$ $$$$ $$36864$$ $$1.1220$$

## Rank

sage: E.rank()

The elliptic curves in class 29400.ba have rank $$1$$.

## Complex multiplication

The elliptic curves in class 29400.ba do not have complex multiplication.

## Modular form 29400.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 2q^{13} - 2q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 