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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 23120bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
23120.c2 | 23120bn1 | \([0, 0, 0, -2227, -59534]\) | \(-60698457/40960\) | \(-824264622080\) | \([]\) | \(59904\) | \(0.98708\) | \(\Gamma_0(N)\)-optimal |
23120.c1 | 23120bn2 | \([0, 0, 0, -2017747, 1103236114]\) | \(-45145776875761017/2441406250\) | \(-49130000000000000\) | \([]\) | \(778752\) | \(2.2696\) |
Rank
sage: E.rank()
The elliptic curves in class 23120bn have rank \(1\).
Complex multiplication
The elliptic curves in class 23120bn do not have complex multiplication.Modular form 23120.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 13 \\ 13 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.