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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 176400bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176400.lb2 | 176400bs1 | \([0, 0, 0, -1155, 16450]\) | \(-9317\) | \(-18289152000\) | \([]\) | \(92160\) | \(0.70748\) | \(\Gamma_0(N)\)-optimal |
176400.lb1 | 176400bs2 | \([0, 0, 0, -29963955, -63131603150]\) | \(-162677523113838677\) | \(-18289152000\) | \([]\) | \(3409920\) | \(2.5129\) |
Rank
sage: E.rank()
The elliptic curves in class 176400bs have rank \(1\).
Complex multiplication
The elliptic curves in class 176400bs do not have complex multiplication.Modular form 176400.2.a.bs
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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.