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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 22743a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
22743.n2 | 22743a1 | \([1, -1, 0, -96, 1547]\) | \(-729/7\) | \(-945039879\) | \([2]\) | \(7680\) | \(0.40458\) | \(\Gamma_0(N)\)-optimal |
22743.n1 | 22743a2 | \([1, -1, 0, -2661, 53360]\) | \(15438249/49\) | \(6615279153\) | \([2]\) | \(15360\) | \(0.75115\) |
Rank
sage: E.rank()
The elliptic curves in class 22743a have rank \(1\).
Complex multiplication
The elliptic curves in class 22743a do not have complex multiplication.Modular form 22743.2.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.