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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 465290t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
465290.t2 | 465290t1 | \([1, -1, 0, -257264, -68061952]\) | \(-78013216986489/37918720000\) | \(-915265720391680000\) | \([2]\) | \(6623232\) | \(2.1520\) | \(\Gamma_0(N)\)-optimal* |
465290.t1 | 465290t2 | \([1, -1, 0, -4511344, -3686582400]\) | \(420676324562824569/56350000000\) | \(1360152013150000000\) | \([2]\) | \(13246464\) | \(2.4986\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 465290t have rank \(0\).
Complex multiplication
The elliptic curves in class 465290t do not have complex multiplication.Modular form 465290.2.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.