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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 29760.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29760.bn1 | 29760ch2 | \([0, 1, 0, -13980641, -20125159521]\) | \(1152829477932246539641/3188367360\) | \(835811373219840\) | \([2]\) | \(798720\) | \(2.5214\) | |
29760.bn2 | 29760ch1 | \([0, 1, 0, -873441, -314937441]\) | \(-281115640967896441/468084326400\) | \(-122705497659801600\) | \([2]\) | \(399360\) | \(2.1749\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 29760.bn have rank \(1\).
Complex multiplication
The elliptic curves in class 29760.bn do not have complex multiplication.Modular form 29760.2.a.bn
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.