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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 400554a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
400554.a2 | 400554a1 | \([1, -1, 0, -1053459, -649718091]\) | \(-7347774183121/6119866368\) | \(-107686929914988576768\) | \([2]\) | \(26492928\) | \(2.5417\) | \(\Gamma_0(N)\)-optimal* |
400554.a1 | 400554a2 | \([1, -1, 0, -19364499, -32785593291]\) | \(45637459887836881/13417633152\) | \(236100534550830778752\) | \([2]\) | \(52985856\) | \(2.8882\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 400554a have rank \(0\).
Complex multiplication
The elliptic curves in class 400554a do not have complex multiplication.Modular form 400554.2.a.a
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.