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Properties

Label 487872.hc
Number of curves $1$
Conductor $487872$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("hc1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 487872.hc1 has rank \(0\).

Complex multiplication

The elliptic curves in class 487872.hc do not have complex multiplication.

Modular form 487872.2.a.hc

Copy content sage:E.q_eigenform(10)
 
\(q - q^{5} + q^{7} + q^{13} + 4 q^{17} + 3 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 487872.hc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
487872.hc1 487872hc1 \([0, 0, 0, -7432788, -7799841016]\) \(-34339609640704/916839\) \(-1212485838059510784\) \([]\) \(11059200\) \(2.5749\) \(\Gamma_0(N)\)-optimal