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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 141120q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.kl2 | 141120q1 | \([0, 0, 0, -147, 167384]\) | \(-64/2205\) | \(-12103314995520\) | \([2]\) | \(294912\) | \(1.1893\) | \(\Gamma_0(N)\)-optimal |
141120.kl1 | 141120q2 | \([0, 0, 0, -46452, 3797696]\) | \(31554496/525\) | \(184431466598400\) | \([2]\) | \(589824\) | \(1.5358\) |
Rank
sage: E.rank()
The elliptic curves in class 141120q have rank \(1\).
Complex multiplication
The elliptic curves in class 141120q do not have complex multiplication.Modular form 141120.2.a.q
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.