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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 7744.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality | CM discriminant |
---|---|---|---|---|---|---|---|---|---|
7744.n1 | 7744s2 | \([0, -1, 0, -3549, 84691]\) | \(-32768\) | \(-150908652224\) | \([]\) | \(6336\) | \(0.92245\) | \(-11\) | |
7744.n2 | 7744s1 | \([0, -1, 0, -29, -53]\) | \(-32768\) | \(-85184\) | \([]\) | \(576\) | \(-0.27650\) | \(\Gamma_0(N)\)-optimal | \(-11\) |
Rank
sage: E.rank()
The elliptic curves in class 7744.n have rank \(0\).
Complex multiplication
Each elliptic curve in class 7744.n has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-11}) \).Modular form 7744.2.a.n
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.