# Properties

 Label 15680.ba Number of curves $3$ Conductor $15680$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 15680.ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
15680.ba1 15680cl3 $$[0, -1, 0, -25741, -1654309]$$ $$-250523582464/13671875$$ $$-102942875000000$$ $$[]$$ $$41472$$ $$1.4470$$
15680.ba2 15680cl1 $$[0, -1, 0, -261, 1891]$$ $$-262144/35$$ $$-263533760$$ $$[]$$ $$4608$$ $$0.34838$$ $$\Gamma_0(N)$$-optimal
15680.ba3 15680cl2 $$[0, -1, 0, 1699, -5165]$$ $$71991296/42875$$ $$-322828856000$$ $$[]$$ $$13824$$ $$0.89769$$

## Rank

sage: E.rank()

The elliptic curves in class 15680.ba have rank $$1$$.

## Complex multiplication

The elliptic curves in class 15680.ba do not have complex multiplication.

## Modular form 15680.2.a.ba

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - 2q^{9} - 3q^{11} + 5q^{13} + q^{15} - 3q^{17} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.