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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 3520d
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3520.q3 | 3520d1 | \([0, 0, 0, -23, 28]\) | \(21024576/6875\) | \(440000\) | \([2]\) | \(256\) | \(-0.21400\) | \(\Gamma_0(N)\)-optimal |
| 3520.q2 | 3520d2 | \([0, 0, 0, -148, -672]\) | \(87528384/3025\) | \(12390400\) | \([2, 2]\) | \(512\) | \(0.13258\) | |
| 3520.q1 | 3520d3 | \([0, 0, 0, -2348, -43792]\) | \(43688592648/55\) | \(1802240\) | \([2]\) | \(1024\) | \(0.47915\) | |
| 3520.q4 | 3520d4 | \([0, 0, 0, 52, -2352]\) | \(474552/73205\) | \(-2398781440\) | \([2]\) | \(1024\) | \(0.47915\) |
Rank
sage: E.rank()
The elliptic curves in class 3520d have rank \(0\).
Complex multiplication
The elliptic curves in class 3520d do not have complex multiplication.Modular form 3520.2.a.d
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.
