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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 309168bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 309168.bc1 | 309168bc1 | \([0, 0, 0, -60375, 5700022]\) | \(130415031250000/262747713\) | \(49035029190912\) | \([2]\) | \(1013760\) | \(1.5140\) | \(\Gamma_0(N)\)-optimal |
| 309168.bc2 | 309168bc2 | \([0, 0, 0, -40035, 9601234]\) | \(-9506392154500/47845660977\) | \(-35716594536686592\) | \([2]\) | \(2027520\) | \(1.8606\) |
Rank
sage: E.rank()
The elliptic curves in class 309168bc have rank \(1\).
Complex multiplication
The elliptic curves in class 309168bc do not have complex multiplication.Modular form 309168.2.a.bc
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.
