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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 302330.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
302330.q1 | 302330q2 | \([1, 1, 0, -2717957, 1768816589]\) | \(-18873978957685236169/580715464000000\) | \(-68320593624136000000\) | \([]\) | \(9704448\) | \(2.5831\) | |
302330.q2 | 302330q1 | \([1, 1, 0, 154178, 9225756]\) | \(3445071928362791/2301874107400\) | \(-270813186861502600\) | \([]\) | \(3234816\) | \(2.0338\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 302330.q have rank \(0\).
Complex multiplication
The elliptic curves in class 302330.q do not have complex multiplication.Modular form 302330.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.