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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 126150n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
126150.c4 | 126150n1 | \([1, 1, 0, -2540, -68100]\) | \(-24389/12\) | \(-892234981500\) | \([2]\) | \(201600\) | \(0.99838\) | \(\Gamma_0(N)\)-optimal |
126150.c2 | 126150n2 | \([1, 1, 0, -44590, -3642350]\) | \(131872229/18\) | \(1338352472250\) | \([2]\) | \(403200\) | \(1.3449\) | |
126150.c3 | 126150n3 | \([1, 1, 0, -23565, 6680925]\) | \(-19465109/248832\) | \(-18501384576384000\) | \([2]\) | \(1008000\) | \(1.8031\) | |
126150.c1 | 126150n4 | \([1, 1, 0, -696365, 222649725]\) | \(502270291349/1889568\) | \(140494889126916000\) | \([2]\) | \(2016000\) | \(2.1497\) |
Rank
sage: E.rank()
The elliptic curves in class 126150n have rank \(0\).
Complex multiplication
The elliptic curves in class 126150n do not have complex multiplication.Modular form 126150.2.a.n
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.