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SageMath
E = EllipticCurve("im1")
E.isogeny_class()
Elliptic curves in class 116160.im
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 116160.im1 | 116160is4 | \([0, 1, 0, -27265, -1726177]\) | \(38614472/405\) | \(23510456893440\) | \([2]\) | \(327680\) | \(1.3823\) | |
| 116160.im2 | 116160is2 | \([0, 1, 0, -3065, 21063]\) | \(438976/225\) | \(1632670617600\) | \([2, 2]\) | \(163840\) | \(1.0357\) | |
| 116160.im3 | 116160is1 | \([0, 1, 0, -2460, 46110]\) | \(14526784/15\) | \(1700698560\) | \([2]\) | \(81920\) | \(0.68911\) | \(\Gamma_0(N)\)-optimal |
| 116160.im4 | 116160is3 | \([0, 1, 0, 11455, 174975]\) | \(2863288/1875\) | \(-108844707840000\) | \([2]\) | \(327680\) | \(1.3823\) |
Rank
sage: E.rank()
The elliptic curves in class 116160.im have rank \(1\).
Complex multiplication
The elliptic curves in class 116160.im do not have complex multiplication.Modular form 116160.2.a.im
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
