# Properties

 Label 31200ba Number of curves $2$ Conductor $31200$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 31200ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.bk2 31200ba1 $$[0, 1, 0, -198, 1008]$$ $$107850176/117$$ $$936000$$ $$$$ $$7168$$ $$0.061373$$ $$\Gamma_0(N)$$-optimal
31200.bk1 31200ba2 $$[0, 1, 0, -248, 408]$$ $$26463592/13689$$ $$876096000$$ $$$$ $$14336$$ $$0.40795$$

## Rank

sage: E.rank()

The elliptic curves in class 31200ba have rank $$1$$.

## Complex multiplication

The elliptic curves in class 31200ba do not have complex multiplication.

## Modular form 31200.2.a.ba

sage: E.q_eigenform(10)

$$q + q^{3} - 4q^{7} + q^{9} + 2q^{11} - q^{13} - 2q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 