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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 301180a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
301180.a4 | 301180a1 | \([0, 1, 0, -62061, 5808160]\) | \(643956736/15125\) | \(620905790978000\) | \([2]\) | \(1866240\) | \(1.6240\) | \(\Gamma_0(N)\)-optimal |
301180.a3 | 301180a2 | \([0, 1, 0, -137356, -11118156]\) | \(436334416/171875\) | \(112891961996000000\) | \([2]\) | \(3732480\) | \(1.9706\) | |
301180.a2 | 301180a3 | \([0, 1, 0, -609661, -181115100]\) | \(610462990336/8857805\) | \(363627267428355920\) | \([2]\) | \(5598720\) | \(2.1733\) | |
301180.a1 | 301180a4 | \([0, 1, 0, -9720356, -11667879356]\) | \(154639330142416/33275\) | \(21855883842425600\) | \([2]\) | \(11197440\) | \(2.5199\) |
Rank
sage: E.rank()
The elliptic curves in class 301180a have rank \(2\).
Complex multiplication
The elliptic curves in class 301180a do not have complex multiplication.Modular form 301180.2.a.a
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.