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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 65366t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
65366.q4 | 65366t1 | \([1, -1, 1, -2205916, -1272100833]\) | \(-10090256344188054273/107965577101312\) | \(-12702042180392255488\) | \([4]\) | \(1843200\) | \(2.4820\) | \(\Gamma_0(N)\)-optimal |
65366.q3 | 65366t2 | \([1, -1, 1, -35384796, -81007585249]\) | \(41647175116728660507393/4693358285056\) | \(552168908878553344\) | \([2, 2]\) | \(3686400\) | \(2.8286\) | |
65366.q2 | 65366t3 | \([1, -1, 1, -35474956, -80573951713]\) | \(41966336340198080824833/442001722607124848\) | \(52001060663005631242352\) | \([2]\) | \(7372800\) | \(3.1752\) | |
65366.q1 | 65366t4 | \([1, -1, 1, -566156716, -5184910367969]\) | \(170586815436843383543017473/2166416\) | \(254876675984\) | \([2]\) | \(7372800\) | \(3.1752\) |
Rank
sage: E.rank()
The elliptic curves in class 65366t have rank \(1\).
Complex multiplication
The elliptic curves in class 65366t do not have complex multiplication.Modular form 65366.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.