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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 121680.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121680.u1 | 121680ch1 | \([0, 0, 0, -113568, -14798992]\) | \(-303464448/1625\) | \(-867435499008000\) | \([]\) | \(580608\) | \(1.7109\) | \(\Gamma_0(N)\)-optimal |
| 121680.u2 | 121680ch2 | \([0, 0, 0, 292032, -78775632]\) | \(7077888/10985\) | \(-4274756836531384320\) | \([]\) | \(1741824\) | \(2.2602\) |
Rank
sage: E.rank()
The elliptic curves in class 121680.u have rank \(0\).
Complex multiplication
The elliptic curves in class 121680.u do not have complex multiplication.Modular form 121680.2.a.u
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.
