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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 2736.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2736.w1 | 2736x2 | \([0, 0, 0, -10083, -431390]\) | \(-37966934881/4952198\) | \(-14787183992832\) | \([]\) | \(7200\) | \(1.2602\) | |
2736.w2 | 2736x1 | \([0, 0, 0, -3, 2050]\) | \(-1/608\) | \(-1815478272\) | \([]\) | \(1440\) | \(0.45552\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 2736.w have rank \(0\).
Complex multiplication
The elliptic curves in class 2736.w do not have complex multiplication.Modular form 2736.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.