Show commands: SageMath
Rank
The elliptic curves in class 68450.u have rank \(1\).
L-function data
Bad L-factors: |
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Good L-factors: |
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See L-function page for more information |
Complex multiplication
The elliptic curves in class 68450.u do not have complex multiplication.Modular form 68450.2.a.u
Isogeny 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
The vertices are labelled with LMFDB labels.
Elliptic curves in class 68450.u
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68450.u1 | 68450f1 | \([1, 1, 0, -16274700, 60383474000]\) | \(-19026212425/51868672\) | \(-1299617397950770000000000\) | \([]\) | \(12312000\) | \(3.3144\) | \(\Gamma_0(N)\)-optimal |
68450.u2 | 68450f2 | \([1, 1, 0, 142015925, -1371038647875]\) | \(12642252501575/39728447488\) | \(-995432879966126080000000000\) | \([]\) | \(36936000\) | \(3.8637\) |