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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 13923.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13923.g1 | 13923g3 | \([1, -1, 0, -222768, 40525195]\) | \(1677087406638588673/4641\) | \(3383289\) | \([2]\) | \(40960\) | \(1.3712\) | |
13923.g2 | 13923g2 | \([1, -1, 0, -13923, 635800]\) | \(409460675852593/21538881\) | \(15701844249\) | \([2, 2]\) | \(20480\) | \(1.0247\) | |
13923.g3 | 13923g4 | \([1, -1, 0, -13158, 708169]\) | \(-345608484635233/94427721297\) | \(-68837808825513\) | \([2]\) | \(40960\) | \(1.3712\) | |
13923.g4 | 13923g1 | \([1, -1, 0, -918, 8959]\) | \(117433042273/22801233\) | \(16622098857\) | \([2]\) | \(10240\) | \(0.67810\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 13923.g have rank \(1\).
Complex multiplication
The elliptic curves in class 13923.g do not have complex multiplication.Modular form 13923.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.