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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 403098.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
403098.y1 | 403098y2 | \([1, 0, 0, -11829025085, 495188632572153]\) | \(1236526859255318155975783969/38367061931916216\) | \(5679702121409274509076024\) | \([]\) | \(322727328\) | \(4.2542\) | \(\Gamma_0(N)\)-optimal* |
403098.y2 | 403098y1 | \([1, 0, 0, -53929445, -151001678847]\) | \(117174888570509216929/1273887851544576\) | \(188581120589701331288064\) | \([]\) | \(46103904\) | \(3.2813\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 403098.y have rank \(1\).
Complex multiplication
The elliptic curves in class 403098.y do not have complex multiplication.Modular form 403098.2.a.y
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.