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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 26010.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26010.l1 | 26010b2 | \([1, -1, 0, -384356760, 2900425560416]\) | \(13217291350697580147/90312500000\) | \(42907448034750937500000\) | \([2]\) | \(5529600\) | \(3.5237\) | |
26010.l2 | 26010b1 | \([1, -1, 0, -23546040, 47206548800]\) | \(-3038732943445107/267267200000\) | \(-126978585416120534400000\) | \([2]\) | \(2764800\) | \(3.1771\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26010.l have rank \(1\).
Complex multiplication
The elliptic curves in class 26010.l do not have complex multiplication.Modular form 26010.2.a.l
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.