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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 95106ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
95106.w2 | 95106ba1 | \([1, 0, 0, -4782, -127566]\) | \(6826561273/7074\) | \(12532022514\) | \([]\) | \(205200\) | \(0.85538\) | \(\Gamma_0(N)\)-optimal |
95106.w1 | 95106ba2 | \([1, 0, 0, -17487, 754161]\) | \(333822098953/53954184\) | \(95583128161224\) | \([]\) | \(615600\) | \(1.4047\) |
Rank
sage: E.rank()
The elliptic curves in class 95106ba have rank \(1\).
Complex multiplication
The elliptic curves in class 95106ba do not have complex multiplication.Modular form 95106.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.