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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 8925.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8925.t1 | 8925bb2 | \([0, 1, 1, -883, -10031]\) | \(121960038400/5055477\) | \(3159673125\) | \([]\) | \(4752\) | \(0.58798\) | |
8925.t2 | 8925bb1 | \([0, 1, 1, -133, 544]\) | \(419430400/3213\) | \(2008125\) | \([3]\) | \(1584\) | \(0.038678\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8925.t have rank \(0\).
Complex multiplication
The elliptic curves in class 8925.t do not have complex multiplication.Modular form 8925.2.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 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.