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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 9450.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9450.z1 | 9450h3 | \([1, -1, 0, -42567, -13650409]\) | \(-3081731187/27343750\) | \(-75685363769531250\) | \([]\) | \(139968\) | \(1.9213\) | |
9450.z2 | 9450h1 | \([1, -1, 0, -4317, 110341]\) | \(-21093208947/17920\) | \(-7560000000\) | \([]\) | \(15552\) | \(0.82272\) | \(\Gamma_0(N)\)-optimal |
9450.z3 | 9450h2 | \([1, -1, 0, 4683, 477341]\) | \(36926037/343000\) | \(-105488578125000\) | \([]\) | \(46656\) | \(1.3720\) |
Rank
sage: E.rank()
The elliptic curves in class 9450.z have rank \(1\).
Complex multiplication
The elliptic curves in class 9450.z do not have complex multiplication.Modular form 9450.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.