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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 106134.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106134.l1 | 106134m2 | \([1, 1, 0, -50908, -4608176]\) | \(-6329617441/279936\) | \(-645321951437184\) | \([]\) | \(508032\) | \(1.6067\) | |
106134.l2 | 106134m1 | \([1, 1, 0, -368, 6126]\) | \(-2401/6\) | \(-13831489014\) | \([]\) | \(72576\) | \(0.63374\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106134.l have rank \(1\).
Complex multiplication
The elliptic curves in class 106134.l do not have complex multiplication.Modular form 106134.2.a.l
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.