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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 4200l
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4200.q4 | 4200l1 | \([0, 1, 0, 217, 438]\) | \(4499456/2835\) | \(-708750000\) | \([4]\) | \(1536\) | \(0.38728\) | \(\Gamma_0(N)\)-optimal |
| 4200.q3 | 4200l2 | \([0, 1, 0, -908, 2688]\) | \(20720464/11025\) | \(44100000000\) | \([2, 2]\) | \(3072\) | \(0.73386\) | |
| 4200.q2 | 4200l3 | \([0, 1, 0, -8408, -297312]\) | \(4108974916/36015\) | \(576240000000\) | \([2]\) | \(6144\) | \(1.0804\) | |
| 4200.q1 | 4200l4 | \([0, 1, 0, -11408, 464688]\) | \(10262905636/13125\) | \(210000000000\) | \([2]\) | \(6144\) | \(1.0804\) |
Rank
sage: E.rank()
The elliptic curves in class 4200l have rank \(0\).
Complex multiplication
The elliptic curves in class 4200l do not have complex multiplication.Modular form 4200.2.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 Cremona 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 Cremona labels.
