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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 30926a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30926.d1 | 30926a1 | \([1, -1, 0, -12446, 147732]\) | \(2053710181431/1101463552\) | \(114357250359296\) | \([2]\) | \(107520\) | \(1.3887\) | \(\Gamma_0(N)\)-optimal |
30926.d2 | 30926a2 | \([1, -1, 0, 47714, 1122324]\) | \(115707762924489/72313663744\) | \(-7507821510893312\) | \([2]\) | \(215040\) | \(1.7353\) |
Rank
sage: E.rank()
The elliptic curves in class 30926a have rank \(0\).
Complex multiplication
The elliptic curves in class 30926a do not have complex multiplication.Modular form 30926.2.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.