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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 292215bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
292215.bj3 | 292215bj1 | \([1, 0, 1, -33883, -2396407]\) | \(2428257525121/8150625\) | \(14439329375625\) | \([2]\) | \(737280\) | \(1.3894\) | \(\Gamma_0(N)\)-optimal |
292215.bj2 | 292215bj2 | \([1, 0, 1, -49008, -49007]\) | \(7347774183121/4251692025\) | \(7532131775501025\) | \([2, 2]\) | \(1474560\) | \(1.7360\) | |
292215.bj1 | 292215bj3 | \([1, 0, 1, -536033, 150539123]\) | \(9614816895690721/34652610405\) | \(61389213141692205\) | \([2]\) | \(2949120\) | \(2.0825\) | |
292215.bj4 | 292215bj4 | \([1, 0, 1, 196017, -343037]\) | \(470166844956479/272118787605\) | \(-482075031488301405\) | \([2]\) | \(2949120\) | \(2.0825\) |
Rank
sage: E.rank()
The elliptic curves in class 292215bj have rank \(1\).
Complex multiplication
The elliptic curves in class 292215bj do not have complex multiplication.Modular form 292215.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.