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SageMath
E = EllipticCurve("bt1")
E.isogeny_class()
Elliptic curves in class 141120.bt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141120.bt1 | 141120di2 | \([0, 0, 0, -1420608, 651721952]\) | \(-225637236736/1715\) | \(-2409904496885760\) | \([]\) | \(1658880\) | \(2.1264\) | |
| 141120.bt2 | 141120di1 | \([0, 0, 0, -9408, 1723232]\) | \(-65536/875\) | \(-1229543110656000\) | \([]\) | \(552960\) | \(1.5771\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.bt have rank \(0\).
Complex multiplication
The elliptic curves in class 141120.bt do not have complex multiplication.Modular form 141120.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
