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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 25350bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25350.z2 | 25350bb1 | \([1, 0, 1, -221901, -42362552]\) | \(-16022066761/998400\) | \(-75298220400000000\) | \([2]\) | \(322560\) | \(1.9925\) | \(\Gamma_0(N)\)-optimal |
25350.z1 | 25350bb2 | \([1, 0, 1, -3601901, -2631442552]\) | \(68523370149961/243360\) | \(18353941222500000\) | \([2]\) | \(645120\) | \(2.3390\) |
Rank
sage: E.rank()
The elliptic curves in class 25350bb have rank \(0\).
Complex multiplication
The elliptic curves in class 25350bb do not have complex multiplication.Modular form 25350.2.a.bb
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.