# Properties

 Label 5915.f Number of curves $3$ Conductor $5915$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 5915.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5915.f1 5915f3 $$[0, 1, 1, -22195, -1338801]$$ $$-250523582464/13671875$$ $$-65991529296875$$ $$[]$$ $$12312$$ $$1.4099$$
5915.f2 5915f1 $$[0, 1, 1, -225, 1369]$$ $$-262144/35$$ $$-168938315$$ $$[]$$ $$1368$$ $$0.31132$$ $$\Gamma_0(N)$$-optimal
5915.f3 5915f2 $$[0, 1, 1, 1465, -3194]$$ $$71991296/42875$$ $$-206949435875$$ $$[]$$ $$4104$$ $$0.86063$$

## Rank

sage: E.rank()

The elliptic curves in class 5915.f have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5915.f do not have complex multiplication.

## Modular form5915.2.a.f

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} + q^{5} - q^{7} - 2q^{9} + 3q^{11} - 2q^{12} + q^{15} + 4q^{16} + 3q^{17} - 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 