# Properties

 Label 5415h Number of curves $2$ Conductor $5415$ CM no Rank $1$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 5415h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5415.c2 5415h1 $$[1, 0, 0, 534, 121371]$$ $$357911/135375$$ $$-6368836140375$$ $$[2]$$ $$8640$$ $$1.1360$$ $$\Gamma_0(N)$$-optimal
5415.c1 5415h2 $$[1, 0, 0, -33761, 2323110]$$ $$90458382169/2671875$$ $$125700713296875$$ $$[2]$$ $$17280$$ $$1.4826$$

## Rank

sage: E.rank()

The elliptic curves in class 5415h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 5415h do not have complex multiplication.

## Modular form5415.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} - 2 q^{7} + 3 q^{8} + q^{9} + q^{10} - 2 q^{11} - q^{12} + 4 q^{13} + 2 q^{14} - q^{15} - q^{16} + 2 q^{17} - q^{18} + O(q^{20})$$

## 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.