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SageMath
E = EllipticCurve("eb1")
E.isogeny_class()
Elliptic curves in class 101430eb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
101430.dk1 | 101430eb1 | \([1, -1, 1, -126747158, 345312170277]\) | \(2625564132023811051529/918925030195200000\) | \(78812635329650176819200000\) | \([2]\) | \(27648000\) | \(3.6705\) | \(\Gamma_0(N)\)-optimal |
101430.dk2 | 101430eb2 | \([1, -1, 1, 379026922, 2413321228581]\) | \(70213095586874240921591/69970703040000000000\) | \(-6001115783383707840000000000\) | \([2]\) | \(55296000\) | \(4.0171\) |
Rank
sage: E.rank()
The elliptic curves in class 101430eb have rank \(1\).
Complex multiplication
The elliptic curves in class 101430eb do not have complex multiplication.Modular form 101430.2.a.eb
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.