# Properties

 Label 152460h Number of curves $2$ Conductor $152460$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 152460h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
152460.cc2 152460h1 $$[0, 0, 0, -23232, 4273841]$$ $$-67108864/343035$$ $$-7088299435934640$$ $$$$ $$921600$$ $$1.7257$$ $$\Gamma_0(N)$$-optimal
152460.cc1 152460h2 $$[0, 0, 0, -562287, 162001334]$$ $$59466754384/121275$$ $$40095431152761600$$ $$$$ $$1843200$$ $$2.0723$$

## Rank

sage: E.rank()

The elliptic curves in class 152460h have rank $$0$$.

## Complex multiplication

The elliptic curves in class 152460h do not have complex multiplication.

## Modular form 152460.2.a.h

sage: E.q_eigenform(10)

$$q + q^{5} + q^{7} + 6q^{13} + 2q^{17} + O(q^{20})$$ ## 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. 