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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 124930g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
124930.g1 | 124930g1 | \([1, 0, 0, -808221, 279562801]\) | \(65787589563409/10400000\) | \(9230038282400000\) | \([2]\) | \(2371200\) | \(2.0739\) | \(\Gamma_0(N)\)-optimal |
124930.g2 | 124930g2 | \([1, 0, 0, -731341, 334901025]\) | \(-48743122863889/26406250000\) | \(-23435644076406250000\) | \([2]\) | \(4742400\) | \(2.4205\) |
Rank
sage: E.rank()
The elliptic curves in class 124930g have rank \(0\).
Complex multiplication
The elliptic curves in class 124930g do not have complex multiplication.Modular form 124930.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.