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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 7350cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7350.cc4 | 7350cc1 | \([1, 1, 1, -148, 881]\) | \(-24389/12\) | \(-176473500\) | \([2]\) | \(2880\) | \(0.28768\) | \(\Gamma_0(N)\)-optimal |
| 7350.cc2 | 7350cc2 | \([1, 1, 1, -2598, 49881]\) | \(131872229/18\) | \(264710250\) | \([2]\) | \(5760\) | \(0.63426\) | |
| 7350.cc3 | 7350cc3 | \([1, 1, 1, -1373, -94669]\) | \(-19465109/248832\) | \(-3659354496000\) | \([2]\) | \(14400\) | \(1.0924\) | |
| 7350.cc1 | 7350cc4 | \([1, 1, 1, -40573, -3152269]\) | \(502270291349/1889568\) | \(27788223204000\) | \([2]\) | \(28800\) | \(1.4390\) |
Rank
sage: E.rank()
The elliptic curves in class 7350cc have rank \(0\).
Complex multiplication
The elliptic curves in class 7350cc do not have complex multiplication.Modular form 7350.2.a.cc
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
