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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 290322.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
290322.g1 | 290322g2 | \([1, -1, 0, -3245960511090, -2250934167609112388]\) | \(1236526859255318155975783969/38367061931916216\) | \(117356837346739225338587634984696\) | \([]\) | \(3338108928\) | \(5.6579\) | |
290322.g2 | 290322g1 | \([1, -1, 0, -14798586330, 686376822727732]\) | \(117174888570509216929/1273887851544576\) | \(3896557147299843960930205433856\) | \([]\) | \(476872704\) | \(4.6849\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 290322.g have rank \(1\).
Complex multiplication
The elliptic curves in class 290322.g do not have complex multiplication.Modular form 290322.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.