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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 126960w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 126960.dg2 | 126960w1 | \([0, 1, 0, 33680, 8008100]\) | \(27871484/198375\) | \(-30071418347904000\) | \([2]\) | \(1419264\) | \(1.8435\) | \(\Gamma_0(N)\)-optimal |
| 126960.dg1 | 126960w2 | \([0, 1, 0, -453000, 107096148]\) | \(33909572018/3234375\) | \(980589728736000000\) | \([2]\) | \(2838528\) | \(2.1901\) |
Rank
sage: E.rank()
The elliptic curves in class 126960w have rank \(0\).
Complex multiplication
The elliptic curves in class 126960w do not have complex multiplication.Modular form 126960.2.a.w
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
