# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("t1")

sage: E.isogeny_class()

## Elliptic curves in class 31200.t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31200.t1 31200bn2 $$[0, -1, 0, -1008, -2988]$$ $$14172488/7605$$ $$60840000000$$ $$$$ $$18432$$ $$0.76048$$
31200.t2 31200bn1 $$[0, -1, 0, 242, -488]$$ $$1560896/975$$ $$-975000000$$ $$$$ $$9216$$ $$0.41391$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 31200.2.a.t

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{7} + q^{9} + q^{13} - 4q^{17} - 2q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 