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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 4830.l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4830.l1 | 4830l4 | \([1, 0, 1, -3014659, 5275646]\) | \(3029968325354577848895529/1753440696000000000000\) | \(1753440696000000000000\) | \([2]\) | \(276480\) | \(2.7658\) | |
4830.l2 | 4830l2 | \([1, 0, 1, -2073844, 1149329042]\) | \(986396822567235411402169/6336721794060000\) | \(6336721794060000\) | \([6]\) | \(92160\) | \(2.2165\) | |
4830.l3 | 4830l1 | \([1, 0, 1, -127124, 18674066]\) | \(-227196402372228188089/19338934824115200\) | \(-19338934824115200\) | \([6]\) | \(46080\) | \(1.8699\) | \(\Gamma_0(N)\)-optimal |
4830.l4 | 4830l3 | \([1, 0, 1, 753661, 753662]\) | \(47342661265381757089751/27397579603968000000\) | \(-27397579603968000000\) | \([2]\) | \(138240\) | \(2.4192\) |
Rank
sage: E.rank()
The elliptic curves in class 4830.l have rank \(0\).
Complex multiplication
The elliptic curves in class 4830.l do not have complex multiplication.Modular form 4830.2.a.l
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.
\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.