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SageMath
E = EllipticCurve("ia1")
E.isogeny_class()
Elliptic curves in class 129600.ia
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129600.ia1 | 129600bt2 | \([0, 0, 0, -360300, -83602000]\) | \(-15590912409/78125\) | \(-25920000000000000\) | \([]\) | \(1032192\) | \(1.9968\) | |
129600.ia2 | 129600bt1 | \([0, 0, 0, -300, 62000]\) | \(-9/5\) | \(-1658880000000\) | \([]\) | \(147456\) | \(1.0238\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 129600.ia have rank \(1\).
Complex multiplication
The elliptic curves in class 129600.ia do not have complex multiplication.Modular form 129600.2.a.ia
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.