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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 129430.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
129430.t1 | 129430r1 | \([1, 1, 1, -60, -205]\) | \(-12932809/70\) | \(-129430\) | \([]\) | \(25704\) | \(-0.17502\) | \(\Gamma_0(N)\)-optimal |
129430.t2 | 129430r2 | \([1, 1, 1, 155, -893]\) | \(222641831/343000\) | \(-634207000\) | \([]\) | \(77112\) | \(0.37429\) |
Rank
sage: E.rank()
The elliptic curves in class 129430.t have rank \(0\).
Complex multiplication
The elliptic curves in class 129430.t do not have complex multiplication.Modular form 129430.2.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.