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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 101430.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.q1 | 101430bh4 | \([1, -1, 0, -43313265, 109728974781]\) | \(104778147797811105409/289854482400\) | \(24859694609910770400\) | \([2]\) | \(7864320\) | \(2.9544\) | |
101430.q2 | 101430bh2 | \([1, -1, 0, -2741265, 1669509981]\) | \(26562019806177409/1343744640000\) | \(115247765387341440000\) | \([2, 2]\) | \(3932160\) | \(2.6078\) | |
101430.q3 | 101430bh1 | \([1, -1, 0, -483345, -95731875]\) | \(145606291302529/37984665600\) | \(3257797425994137600\) | \([2]\) | \(1966080\) | \(2.2613\) | \(\Gamma_0(N)\)-optimal |
101430.q4 | 101430bh3 | \([1, -1, 0, 1704015, 6558428925]\) | \(6380108151242111/220374787500000\) | \(-18900690690074287500000\) | \([2]\) | \(7864320\) | \(2.9544\) |
Rank
sage: E.rank()
The elliptic curves in class 101430.q have rank \(0\).
Complex multiplication
The elliptic curves in class 101430.q do not have complex multiplication.Modular form 101430.2.a.q
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.