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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 18810.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
18810.l1 | 18810m2 | \([1, -1, 0, -3879, 93933]\) | \(8855610342769/3494480\) | \(2547475920\) | \([2]\) | \(18432\) | \(0.76923\) | |
18810.l2 | 18810m1 | \([1, -1, 0, -279, 1053]\) | \(3301293169/1337600\) | \(975110400\) | \([2]\) | \(9216\) | \(0.42265\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18810.l have rank \(1\).
Complex multiplication
The elliptic curves in class 18810.l do not have complex multiplication.Modular form 18810.2.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.