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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 96192.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96192.x1 | 96192y2 | \([0, 0, 0, -71724, -7373360]\) | \(213525509833/669336\) | \(127912101543936\) | \([2]\) | \(442368\) | \(1.5742\) | |
| 96192.x2 | 96192y1 | \([0, 0, 0, -2604, -212528]\) | \(-10218313/96192\) | \(-18382577467392\) | \([2]\) | \(221184\) | \(1.2276\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 96192.x have rank \(0\).
Complex multiplication
The elliptic curves in class 96192.x do not have complex multiplication.Modular form 96192.2.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.
