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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 17325w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17325.bn4 | 17325w1 | \([1, -1, 0, -792, 62491]\) | \(-4826809/144375\) | \(-1644521484375\) | \([2]\) | \(18432\) | \(1.0245\) | \(\Gamma_0(N)\)-optimal |
| 17325.bn3 | 17325w2 | \([1, -1, 0, -28917, 1890616]\) | \(234770924809/1334025\) | \(15195378515625\) | \([2, 2]\) | \(36864\) | \(1.3710\) | |
| 17325.bn2 | 17325w3 | \([1, -1, 0, -45792, -556259]\) | \(932288503609/527295615\) | \(6006226614609375\) | \([2]\) | \(73728\) | \(1.7176\) | |
| 17325.bn1 | 17325w4 | \([1, -1, 0, -462042, 120999991]\) | \(957681397954009/31185\) | \(355216640625\) | \([2]\) | \(73728\) | \(1.7176\) |
Rank
sage: E.rank()
The elliptic curves in class 17325w have rank \(1\).
Complex multiplication
The elliptic curves in class 17325w do not have complex multiplication.Modular form 17325.2.a.w
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.
