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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 57222t
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 57222.z2 | 57222t1 | \([1, -1, 0, -1071058041, 12968401028589]\) | \(7722211175253055152433/340131399900069888\) | \(5985050002798652389261836288\) | \([2]\) | \(37380096\) | \(4.0930\) | \(\Gamma_0(N)\)-optimal |
| 57222.z1 | 57222t2 | \([1, -1, 0, -2882186361, -42453212240403]\) | \(150476552140919246594353/42832838728685592576\) | \(753698957603770641409524965376\) | \([2]\) | \(74760192\) | \(4.4396\) |
Rank
sage: E.rank()
The elliptic curves in class 57222t have rank \(1\).
Complex multiplication
The elliptic curves in class 57222t do not have complex multiplication.Modular form 57222.2.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.
