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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 38025bt
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
38025.b2 | 38025bt1 | \([0, 0, 1, 2535, -216954]\) | \(20480/243\) | \(-21376368348075\) | \([]\) | \(112320\) | \(1.2387\) | \(\Gamma_0(N)\)-optimal |
38025.b1 | 38025bt2 | \([0, 0, 1, -316875, 70372656]\) | \(-102400/3\) | \(-103088196123046875\) | \([]\) | \(561600\) | \(2.0434\) |
Rank
sage: E.rank()
The elliptic curves in class 38025bt have rank \(0\).
Complex multiplication
The elliptic curves in class 38025bt do not have complex multiplication.Modular form 38025.2.a.bt
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.