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SageMath
E = EllipticCurve("t1")
E.isogeny_class()
Elliptic curves in class 4950t
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4950.q2 | 4950t1 | \([1, -1, 0, -252, 1606]\) | \(-19465109/22\) | \(-2004750\) | \([]\) | \(1440\) | \(0.12300\) | \(\Gamma_0(N)\)-optimal |
4950.q3 | 4950t2 | \([1, -1, 0, 1773, -16619]\) | \(6761990971/5153632\) | \(-469624716000\) | \([]\) | \(7200\) | \(0.92772\) | |
4950.q1 | 4950t3 | \([1, -1, 0, -272952, -54820544]\) | \(-24680042791780949/369098752\) | \(-33634123776000\) | \([]\) | \(36000\) | \(1.7324\) |
Rank
sage: E.rank()
The elliptic curves in class 4950t have rank \(1\).
Complex multiplication
The elliptic curves in class 4950t do not have complex multiplication.Modular form 4950.2.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.
\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.