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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 930g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
930.g3 | 930g1 | \([1, 0, 1, -244, 1442]\) | \(1597099875769/186000\) | \(186000\) | \([2]\) | \(288\) | \(0.037436\) | \(\Gamma_0(N)\)-optimal |
930.g2 | 930g2 | \([1, 0, 1, -264, 1186]\) | \(2023804595449/540562500\) | \(540562500\) | \([2, 2]\) | \(576\) | \(0.38401\) | |
930.g1 | 930g3 | \([1, 0, 1, -1514, -21814]\) | \(383432500775449/18701300250\) | \(18701300250\) | \([2]\) | \(1152\) | \(0.73058\) | |
930.g4 | 930g4 | \([1, 0, 1, 666, 7882]\) | \(32740359775271/45410156250\) | \(-45410156250\) | \([2]\) | \(1152\) | \(0.73058\) |
Rank
sage: E.rank()
The elliptic curves in class 930g have rank \(0\).
Complex multiplication
The elliptic curves in class 930g do not have complex multiplication.Modular form 930.2.a.g
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.