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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 265200.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
265200.w1 | 265200w2 | \([0, -1, 0, -1183208, 495776112]\) | \(-71559517896165625/4598568\) | \(-11772334080000\) | \([]\) | \(2115072\) | \(1.9670\) | |
265200.w2 | 265200w1 | \([0, -1, 0, -13208, 819312]\) | \(-99546915625/54454842\) | \(-139404395520000\) | \([]\) | \(705024\) | \(1.4177\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 265200.w have rank \(2\).
Complex multiplication
The elliptic curves in class 265200.w do not have complex multiplication.Modular form 265200.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.