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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 85176.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85176.x1 | 85176g2 | \([0, 0, 0, -296595, 61634638]\) | \(4920750/49\) | \(28732933469140992\) | \([2]\) | \(678912\) | \(1.9767\) | |
| 85176.x2 | 85176g1 | \([0, 0, 0, -32955, -742586]\) | \(13500/7\) | \(2052352390652928\) | \([2]\) | \(339456\) | \(1.6301\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 85176.x have rank \(0\).
Complex multiplication
The elliptic curves in class 85176.x do not have complex multiplication.Modular form 85176.2.a.x
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.
