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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 26010.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26010.d1 | 26010m2 | \([1, -1, 0, -405810, -88534134]\) | \(420021471169/50191650\) | \(883186718607061650\) | \([2]\) | \(368640\) | \(2.1745\) | |
26010.d2 | 26010m1 | \([1, -1, 0, 36360, -7086420]\) | \(302111711/1404540\) | \(-24714690068016540\) | \([2]\) | \(184320\) | \(1.8279\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 26010.d have rank \(0\).
Complex multiplication
The elliptic curves in class 26010.d do not have complex multiplication.Modular form 26010.2.a.d
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.