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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 26640ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26640.z2 | 26640ce1 | \([0, 0, 0, -147, 8786]\) | \(-117649/11100\) | \(-33144422400\) | \([2]\) | \(15360\) | \(0.69825\) | \(\Gamma_0(N)\)-optimal |
26640.z1 | 26640ce2 | \([0, 0, 0, -7347, 240626]\) | \(14688124849/123210\) | \(367903088640\) | \([2]\) | \(30720\) | \(1.0448\) |
Rank
sage: E.rank()
The elliptic curves in class 26640ce have rank \(1\).
Complex multiplication
The elliptic curves in class 26640ce do not have complex multiplication.Modular form 26640.2.a.ce
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.