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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 3150.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3150.z1 | 3150z2 | \([1, -1, 1, -20465, 1131937]\) | \(280844088456303/614656\) | \(2074464000\) | \([2]\) | \(6144\) | \(1.0341\) | |
3150.z2 | 3150z1 | \([1, -1, 1, -1265, 18337]\) | \(-66282611823/3211264\) | \(-10838016000\) | \([2]\) | \(3072\) | \(0.68754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3150.z have rank \(1\).
Complex multiplication
The elliptic curves in class 3150.z do not have complex multiplication.Modular form 3150.2.a.z
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.