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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 205350.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205350.i1 | 205350dy2 | \([1, 1, 0, -9684075, 11599552125]\) | \(-203045327257525/84934656\) | \(-42013624320000000000\) | \([]\) | \(12096000\) | \(2.7269\) | |
205350.i2 | 205350dy1 | \([1, 1, 0, 101130, -3168540]\) | \(90325805449595/55788550416\) | \(-70646436105541200\) | \([]\) | \(2419200\) | \(1.9222\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 205350.i have rank \(0\).
Complex multiplication
The elliptic curves in class 205350.i do not have complex multiplication.Modular form 205350.2.a.i
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.