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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 52094.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
52094.g1 | 52094j6 | \([1, 0, 0, -10160268, -12466236272]\) | \(2251439055699625/25088\) | \(1292543151968768\) | \([2]\) | \(1360800\) | \(2.4685\) | |
52094.g2 | 52094j5 | \([1, 0, 0, -634508, -195152240]\) | \(-548347731625/1835008\) | \(-94540299115429888\) | \([2]\) | \(680400\) | \(2.1220\) | |
52094.g3 | 52094j4 | \([1, 0, 0, -132173, -15171191]\) | \(4956477625/941192\) | \(48490564185578312\) | \([2]\) | \(453600\) | \(1.9192\) | |
52094.g4 | 52094j2 | \([1, 0, 0, -39148, 2976126]\) | \(128787625/98\) | \(5048996687378\) | \([2]\) | \(151200\) | \(1.3699\) | |
52094.g5 | 52094j1 | \([1, 0, 0, -1938, 66304]\) | \(-15625/28\) | \(-1442570482108\) | \([2]\) | \(75600\) | \(1.0234\) | \(\Gamma_0(N)\)-optimal |
52094.g6 | 52094j3 | \([1, 0, 0, 16667, -1388607]\) | \(9938375/21952\) | \(-1130975257972672\) | \([2]\) | \(226800\) | \(1.5727\) |
Rank
sage: E.rank()
The elliptic curves in class 52094.g have rank \(0\).
Complex multiplication
The elliptic curves in class 52094.g do not have complex multiplication.Modular form 52094.2.a.g
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.
\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.