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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 28050.cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28050.cc1 | 28050by4 | \([1, 1, 1, -60433813, -135935406469]\) | \(1562225332123379392365961/393363080510106009600\) | \(6146298132970406400000000\) | \([2]\) | \(6635520\) | \(3.4664\) | |
| 28050.cc2 | 28050by2 | \([1, 1, 1, -20749438, 36357893531]\) | \(63229930193881628103961/26218934428500000\) | \(409670850445312500000\) | \([2]\) | \(2211840\) | \(2.9171\) | |
| 28050.cc3 | 28050by1 | \([1, 1, 1, -1097438, 748469531]\) | \(-9354997870579612441/10093752054144000\) | \(-157714875846000000000\) | \([2]\) | \(1105920\) | \(2.5705\) | \(\Gamma_0(N)\)-optimal |
| 28050.cc4 | 28050by3 | \([1, 1, 1, 9198187, -13522350469]\) | \(5508208700580085578359/8246033269590589440\) | \(-128844269837352960000000\) | \([2]\) | \(3317760\) | \(3.1198\) |
Rank
sage: E.rank()
The elliptic curves in class 28050.cc have rank \(0\).
Complex multiplication
The elliptic curves in class 28050.cc do not have complex multiplication.Modular form 28050.2.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 LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
