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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 167334.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
167334.e1 | 167334h2 | \([1, 0, 1, -3472762, 2483879540]\) | \(213525509833/669336\) | \(14519210807067240984\) | \([2]\) | \(8031744\) | \(2.5441\) | |
167334.e2 | 167334h1 | \([1, 0, 1, -126082, 71592596]\) | \(-10218313/96192\) | \(-2086593169877926848\) | \([2]\) | \(4015872\) | \(2.1976\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 167334.e have rank \(1\).
Complex multiplication
The elliptic curves in class 167334.e do not have complex multiplication.Modular form 167334.2.a.e
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.