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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 18513.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18513.g1 | 18513q3 | \([1, -1, 1, -98759, -11920994]\) | \(82483294977/17\) | \(21954955473\) | \([2]\) | \(46080\) | \(1.3716\) | |
18513.g2 | 18513q2 | \([1, -1, 1, -6194, -183752]\) | \(20346417/289\) | \(373234243041\) | \([2, 2]\) | \(23040\) | \(1.0250\) | |
18513.g3 | 18513q4 | \([1, -1, 1, -749, -499562]\) | \(-35937/83521\) | \(-107864696238849\) | \([2]\) | \(46080\) | \(1.3716\) | |
18513.g4 | 18513q1 | \([1, -1, 1, -749, 3556]\) | \(35937/17\) | \(21954955473\) | \([2]\) | \(11520\) | \(0.67847\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18513.g have rank \(0\).
Complex multiplication
The elliptic curves in class 18513.g do not have complex multiplication.Modular form 18513.2.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.