# Properties

 Label 158400mg Number of curves 2 Conductor 158400 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("158400.lt1")

sage: E.isogeny_class()

## Elliptic curves in class 158400mg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
158400.lt2 158400mg1 [0, 0, 0, 2400, 25000]  196608 $$\Gamma_0(N)$$-optimal
158400.lt1 158400mg2 [0, 0, 0, -11100, 214000]  393216

## Rank

sage: E.rank()

The elliptic curves in class 158400mg have rank $$1$$.

## Modular form 158400.2.a.lt

sage: E.q_eigenform(10)

$$q + 2q^{7} + q^{11} - 2q^{13} + 4q^{17} + 6q^{19} + O(q^{20})$$

## 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 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. 