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SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 440818.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
440818.y1 | 440818y2 | \([1, 1, 1, -1142792629, 14869114094131]\) | \(64330312237537307644873/44231104389416\) | \(113484912631160451287144\) | \([2]\) | \(168099840\) | \(3.7385\) | \(\Gamma_0(N)\)-optimal* |
440818.y2 | 440818y1 | \([1, 1, 1, -70975149, 235375676195]\) | \(-15411052746525070153/412083253984192\) | \(-1057292887453895882926528\) | \([2]\) | \(84049920\) | \(3.3919\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 440818.y have rank \(1\).
Complex multiplication
The elliptic curves in class 440818.y do not have complex multiplication.Modular form 440818.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.