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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 112896.ci
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality | CM discriminant |
---|---|---|---|---|---|---|---|---|---|
112896.ci1 | 112896bi2 | \([0, 0, 0, -5880, -153664]\) | \(8000\) | \(2810384252928\) | \([2]\) | \(147456\) | \(1.1183\) | \(-8\) | |
112896.ci2 | 112896bi1 | \([0, 0, 0, -1470, 19208]\) | \(8000\) | \(43912253952\) | \([2]\) | \(73728\) | \(0.77172\) | \(\Gamma_0(N)\)-optimal | \(-8\) |
Rank
sage: E.rank()
The elliptic curves in class 112896.ci have rank \(1\).
Complex multiplication
Each elliptic curve in class 112896.ci has complex multiplication by an order in the imaginary quadratic field \(\Q(\sqrt{-2}) \).Modular form 112896.2.a.ci
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.