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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 37026l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
37026.e2 | 37026l1 | \([1, -1, 0, -288063, -2869619]\) | \(2046931732873/1181672448\) | \(1526092116441818112\) | \([2]\) | \(460800\) | \(2.1786\) | \(\Gamma_0(N)\)-optimal |
37026.e1 | 37026l2 | \([1, -1, 0, -3250143, -2248718675]\) | \(2940001530995593/8673562656\) | \(11201628347338565664\) | \([2]\) | \(921600\) | \(2.5252\) |
Rank
sage: E.rank()
The elliptic curves in class 37026l have rank \(1\).
Complex multiplication
The elliptic curves in class 37026l do not have complex multiplication.Modular form 37026.2.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 Cremona 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 Cremona labels.