Properties

Label 428400.mr
Number of curves $1$
Conductor $428400$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("mr1")
 
E.isogeny_class()
 

Elliptic curves in class 428400.mr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
428400.mr1 428400mr1 \([0, 0, 0, -17135464800, 863500557278000]\) \(-11926249134908509075308544/2246680441062421875\) \(-104821122658208355000000000000\) \([]\) \(580608000\) \(4.5700\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 428400.mr1 has rank \(1\).

Complex multiplication

The elliptic curves in class 428400.mr do not have complex multiplication.

Modular form 428400.2.a.mr

sage: E.q_eigenform(10)
 
\(q + q^{7} + 2 q^{11} + 5 q^{13} + q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display