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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 54978bs
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54978.bn1 | 54978bs1 | \([1, 1, 1, -9703, -371911]\) | \(858729462625/38148\) | \(4488074052\) | \([2]\) | \(92160\) | \(0.92938\) | \(\Gamma_0(N)\)-optimal |
54978.bn2 | 54978bs2 | \([1, 1, 1, -9213, -410523]\) | \(-735091890625/181908738\) | \(-21401381116962\) | \([2]\) | \(184320\) | \(1.2760\) |
Rank
sage: E.rank()
The elliptic curves in class 54978bs have rank \(1\).
Complex multiplication
The elliptic curves in class 54978bs do not have complex multiplication.Modular form 54978.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.