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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 832.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
832.j1 | 832f2 | \([0, 0, 0, -13612, -670672]\) | \(-1064019559329/125497034\) | \(-32898294480896\) | \([]\) | \(2688\) | \(1.3295\) | |
832.j2 | 832f1 | \([0, 0, 0, -172, 1328]\) | \(-2146689/1664\) | \(-436207616\) | \([]\) | \(384\) | \(0.35656\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 832.j have rank \(0\).
Complex multiplication
The elliptic curves in class 832.j do not have complex multiplication.Modular form 832.2.a.j
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.