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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 67158.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
67158.l1 | 67158l2 | \([1, -1, 0, -13587, -505333]\) | \(380526485144625/66845573522\) | \(48730423097538\) | \([2]\) | \(208896\) | \(1.3462\) | |
67158.l2 | 67158l1 | \([1, -1, 0, 1623, -45991]\) | \(648337611375/1606613372\) | \(-1171221148188\) | \([2]\) | \(104448\) | \(0.99960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 67158.l have rank \(1\).
Complex multiplication
The elliptic curves in class 67158.l do not have complex multiplication.Modular form 67158.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.