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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 152460t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
152460.s2 | 152460t1 | \([0, 0, 0, 59532, 59952233]\) | \(1129201664/75796875\) | \(-1566227779404750000\) | \([2]\) | \(1658880\) | \(2.1708\) | \(\Gamma_0(N)\)-optimal |
152460.s1 | 152460t2 | \([0, 0, 0, -1982343, 1034743358]\) | \(2605772594896/108945375\) | \(36019062318897504000\) | \([2]\) | \(3317760\) | \(2.5174\) |
Rank
sage: E.rank()
The elliptic curves in class 152460t have rank \(1\).
Complex multiplication
The elliptic curves in class 152460t 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 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.