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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 155682.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155682.g1 | 155682o3 | \([1, -1, 0, -1035177, -405128755]\) | \(-189613868625/128\) | \(-82814743481472\) | \([]\) | \(1270080\) | \(1.9864\) | |
155682.g2 | 155682o4 | \([1, -1, 0, -818952, -579259072]\) | \(-1159088625/2097152\) | \(-109903777333235417088\) | \([]\) | \(3810240\) | \(2.5357\) | |
155682.g3 | 155682o2 | \([1, -1, 0, -40542, 3302972]\) | \(-140625/8\) | \(-419249638874952\) | \([]\) | \(544320\) | \(1.5627\) | |
155682.g4 | 155682o1 | \([1, -1, 0, 2703, 7703]\) | \(3375/2\) | \(-1293980366898\) | \([]\) | \(181440\) | \(1.0134\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 155682.g have rank \(1\).
Complex multiplication
The elliptic curves in class 155682.g do not have complex multiplication.Modular form 155682.2.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.
\(\left(\begin{array}{rrrr} 1 & 3 & 21 & 7 \\ 3 & 1 & 7 & 21 \\ 21 & 7 & 1 & 3 \\ 7 & 21 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.