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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 263568.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
263568.cb1 | 263568cb3 | \([0, 1, 0, -1979168, 1071028980]\) | \(8671983378625/82308\) | \(8137584759816192\) | \([2]\) | \(3981312\) | \(2.2153\) | |
263568.cb2 | 263568cb4 | \([0, 1, 0, -1932928, 1123502132]\) | \(-8078253774625/846825858\) | \(-83723540801368891392\) | \([2]\) | \(7962624\) | \(2.5618\) | |
263568.cb3 | 263568cb1 | \([0, 1, 0, -37088, -222348]\) | \(57066625/32832\) | \(3246017189511168\) | \([2]\) | \(1327104\) | \(1.6659\) | \(\Gamma_0(N)\)-optimal |
263568.cb4 | 263568cb2 | \([0, 1, 0, 147872, -1628044]\) | \(3616805375/2105352\) | \(-208150852277403648\) | \([2]\) | \(2654208\) | \(2.0125\) |
Rank
sage: E.rank()
The elliptic curves in class 263568.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 263568.cb do not have complex multiplication.Modular form 263568.2.a.cb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.