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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 11109.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
11109.g1 | 11109c2 | \([1, 0, 1, -8786, -296215]\) | \(6163717745375/466948881\) | \(5681367035127\) | \([2]\) | \(16896\) | \(1.1924\) | |
11109.g2 | 11109c1 | \([1, 0, 1, 529, -20491]\) | \(1349232625/15752961\) | \(-191666276487\) | \([2]\) | \(8448\) | \(0.84585\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11109.g have rank \(1\).
Complex multiplication
The elliptic curves in class 11109.g do not have complex multiplication.Modular form 11109.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.