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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 9450.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9450.cu1 | 9450ce1 | \([1, -1, 1, -3530, 81597]\) | \(-11527859979/28\) | \(-11812500\) | \([]\) | \(7776\) | \(0.59736\) | \(\Gamma_0(N)\)-optimal |
| 9450.cu2 | 9450ce2 | \([1, -1, 1, -2405, 133597]\) | \(-5000211/21952\) | \(-6751269000000\) | \([]\) | \(23328\) | \(1.1467\) | |
| 9450.cu3 | 9450ce3 | \([1, -1, 1, 21220, -3221153]\) | \(381790581/1835008\) | \(-5079158784000000\) | \([]\) | \(69984\) | \(1.6960\) |
Rank
sage: E.rank()
The elliptic curves in class 9450.cu have rank \(0\).
Complex multiplication
The elliptic curves in class 9450.cu do not have complex multiplication.Modular form 9450.2.a.cu
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
