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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 46410.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46410.p1 | 46410n4 | \([1, 1, 0, -740012, -245331216]\) | \(44816807438220995641801/9512718589920\) | \(9512718589920\) | \([2]\) | \(491520\) | \(1.8758\) | |
| 46410.p2 | 46410n3 | \([1, 1, 0, -90092, 4453296]\) | \(80870462846141298121/38087635627860000\) | \(38087635627860000\) | \([2]\) | \(491520\) | \(1.8758\) | |
| 46410.p3 | 46410n2 | \([1, 1, 0, -46412, -3819696]\) | \(11056793118237203401/159353257190400\) | \(159353257190400\) | \([2, 2]\) | \(245760\) | \(1.5292\) | |
| 46410.p4 | 46410n1 | \([1, 1, 0, -332, -160944]\) | \(-4066120948681/11168482590720\) | \(-11168482590720\) | \([2]\) | \(122880\) | \(1.1826\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 46410.p have rank \(1\).
Complex multiplication
The elliptic curves in class 46410.p do not have complex multiplication.Modular form 46410.2.a.p
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
