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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 116688t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116688.o1 | 116688t1 | \([0, -1, 0, -88561, 10173628]\) | \(4801049335176577024/6222978333\) | \(99567653328\) | \([2]\) | \(571392\) | \(1.3874\) | \(\Gamma_0(N)\)-optimal |
| 116688.o2 | 116688t2 | \([0, -1, 0, -87796, 10357228]\) | \(-292356586786125904/10812404517057\) | \(-2767975556366592\) | \([2]\) | \(1142784\) | \(1.7340\) |
Rank
sage: E.rank()
The elliptic curves in class 116688t have rank \(0\).
Complex multiplication
The elliptic curves in class 116688t do not have complex multiplication.Modular form 116688.2.a.t
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 Cremona 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 Cremona labels.
