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SageMath
E = EllipticCurve("dc1")
E.isogeny_class()
Elliptic curves in class 200400dc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 200400.l4 | 200400dc1 | \([0, -1, 0, -134383, 17037262]\) | \(1073544204384256/122314453125\) | \(30578613281250000\) | \([2]\) | \(1520640\) | \(1.8956\) | \(\Gamma_0(N)\)-optimal |
| 200400.l2 | 200400dc2 | \([0, -1, 0, -2087508, 1161568512]\) | \(251506014024024016/3921890625\) | \(15687562500000000\) | \([2, 2]\) | \(3041280\) | \(2.2422\) | |
| 200400.l1 | 200400dc3 | \([0, -1, 0, -33400008, 74307568512]\) | \(257539266816816096004/62625\) | \(1002000000000\) | \([4]\) | \(6082560\) | \(2.5888\) | |
| 200400.l3 | 200400dc4 | \([0, -1, 0, -2025008, 1234318512]\) | \(-57396336590916004/7875187750125\) | \(-126003004002000000000\) | \([2]\) | \(6082560\) | \(2.5888\) |
Rank
sage: E.rank()
The elliptic curves in class 200400dc have rank \(1\).
Complex multiplication
The elliptic curves in class 200400dc do not have complex multiplication.Modular form 200400.2.a.dc
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.
