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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 76050.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.q1 | 76050cd2 | \([1, -1, 0, -12244842, -16764588684]\) | \(-1680914269/32768\) | \(-3958108181973504000000\) | \([]\) | \(5054400\) | \(2.9376\) | |
| 76050.q2 | 76050cd1 | \([1, -1, 0, 113283, 44932941]\) | \(1331/8\) | \(-966335005364625000\) | \([]\) | \(1010880\) | \(2.1329\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76050.q have rank \(1\).
Complex multiplication
The elliptic curves in class 76050.q do not have complex multiplication.Modular form 76050.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
