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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 27225.ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality | CM discriminant |
---|---|---|---|---|---|---|---|---|---|
27225.ba1 | 27225ba2 | \([0, 0, 1, -199650, 35229906]\) | \(-32768\) | \(-26858497917796875\) | \([]\) | \(142560\) | \(1.9299\) | \(-11\) | |
27225.ba2 | 27225ba1 | \([0, 0, 1, -1650, -26469]\) | \(-32768\) | \(-15160921875\) | \([]\) | \(12960\) | \(0.73095\) | \(\Gamma_0(N)\)-optimal | \(-11\) |
Rank
sage: E.rank()
The elliptic curves in class 27225.ba have rank \(0\).
Complex multiplication
Each elliptic curve in class 27225.ba has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).Modular form 27225.2.a.ba
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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.