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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 152460.t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152460.t1 | 152460u2 | \([0, 0, 0, -51183, 3090582]\) | \(44851536/13475\) | \(4455047905862400\) | \([2]\) | \(737280\) | \(1.7080\) | |
152460.t2 | 152460u1 | \([0, 0, 0, 8712, 323433]\) | \(3538944/4235\) | \(-87509869579440\) | \([2]\) | \(368640\) | \(1.3614\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 152460.t have rank \(1\).
Complex multiplication
The elliptic curves in class 152460.t do not have complex multiplication.Modular form 152460.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.