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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 414050l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414050.l2 | 414050l1 | \([1, 0, 1, -1356, -16222]\) | \(46585/8\) | \(47302728200\) | \([]\) | \(497664\) | \(0.76869\) | \(\Gamma_0(N)\)-optimal* |
414050.l1 | 414050l2 | \([1, 0, 1, -30931, 2089518]\) | \(553463785/512\) | \(3027374604800\) | \([]\) | \(1492992\) | \(1.3180\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414050l have rank \(0\).
Complex multiplication
The elliptic curves in class 414050l do not have complex multiplication.Modular form 414050.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.