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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 277200.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
277200.q1 | 277200q1 | \([0, 0, 0, -14250, -340625]\) | \(14047232/5929\) | \(135070031250000\) | \([2]\) | \(921600\) | \(1.4082\) | \(\Gamma_0(N)\)-optimal |
277200.q2 | 277200q2 | \([0, 0, 0, 47625, -2506250]\) | \(32774128/26411\) | \(-9626809500000000\) | \([2]\) | \(1843200\) | \(1.7548\) |
Rank
sage: E.rank()
The elliptic curves in class 277200.q have rank \(1\).
Complex multiplication
The elliptic curves in class 277200.q do not have complex multiplication.Modular form 277200.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.