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SageMath
E = EllipticCurve("gq1")
E.isogeny_class()
Elliptic curves in class 92400.gq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
92400.gq1 | 92400cl4 | \([0, 1, 0, -251533408, -1535554874812]\) | \(109999511474021786850916/38201625\) | \(611226000000000\) | \([2]\) | \(8847360\) | \(3.0985\) | |
92400.gq2 | 92400cl2 | \([0, 1, 0, -15720908, -23996749812]\) | \(107422839278466723664/2001871265625\) | \(8007485062500000000\) | \([2, 2]\) | \(4423680\) | \(2.7519\) | |
92400.gq3 | 92400cl3 | \([0, 1, 0, -15206408, -25640062812]\) | \(-24304331176056594436/3678122314453125\) | \(-58849957031250000000000\) | \([2]\) | \(8847360\) | \(3.0985\) | |
92400.gq4 | 92400cl1 | \([0, 1, 0, -1014783, -349300812]\) | \(462278484549842944/57095309704125\) | \(14273827426031250000\) | \([2]\) | \(2211840\) | \(2.4054\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 92400.gq have rank \(1\).
Complex multiplication
The elliptic curves in class 92400.gq do not have complex multiplication.Modular form 92400.2.a.gq
sage: E.q_eigenform(10)
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.