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SageMath
E = EllipticCurve("cc1")
E.isogeny_class()
Elliptic curves in class 61200cc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61200.t3 | 61200cc1 | \([0, 0, 0, -11775, 490750]\) | \(61918288/153\) | \(446148000000\) | \([2]\) | \(131072\) | \(1.1132\) | \(\Gamma_0(N)\)-optimal |
| 61200.t2 | 61200cc2 | \([0, 0, 0, -16275, 81250]\) | \(40873252/23409\) | \(273042576000000\) | \([2, 2]\) | \(262144\) | \(1.4598\) | |
| 61200.t4 | 61200cc3 | \([0, 0, 0, 64725, 648250]\) | \(1285471294/751689\) | \(-17535400992000000\) | \([2]\) | \(524288\) | \(1.8063\) | |
| 61200.t1 | 61200cc4 | \([0, 0, 0, -169275, -26693750]\) | \(22994537186/111537\) | \(2601935136000000\) | \([2]\) | \(524288\) | \(1.8063\) |
Rank
sage: E.rank()
The elliptic curves in class 61200cc have rank \(1\).
Complex multiplication
The elliptic curves in class 61200cc do not have complex multiplication.Modular form 61200.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
