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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 348726cb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 348726.cb4 | 348726cb1 | \([1, 1, 1, 1676657, -5884372843]\) | \(11079872671250375/324440155855872\) | \(-15263572964016807263232\) | \([2]\) | \(34214400\) | \(2.9367\) | \(\Gamma_0(N)\)-optimal |
| 348726.cb2 | 348726cb2 | \([1, 1, 1, -40430383, -94292314027]\) | \(155355156733986861625/8291568305839392\) | \(390084135819891641144352\) | \([2]\) | \(68428800\) | \(3.2833\) | |
| 348726.cb3 | 348726cb3 | \([1, 1, 1, -15136918, 161682405779]\) | \(-8152944444844179625/235342826399858688\) | \(-11071910605011410252464128\) | \([2]\) | \(102643200\) | \(3.4860\) | |
| 348726.cb1 | 348726cb4 | \([1, 1, 1, -547453078, 4906109876627]\) | \(385693937170561837203625/2159357734550274048\) | \(101588887016081781379596288\) | \([2]\) | \(205286400\) | \(3.8326\) |
Rank
sage: E.rank()
The elliptic curves in class 348726cb have rank \(1\).
Complex multiplication
The elliptic curves in class 348726cb do not have complex multiplication.Modular form 348726.2.a.cb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
