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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 17457a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17457.c3 | 17457a1 | \([1, 1, 0, -3449, 75888]\) | \(30664297/297\) | \(43966659033\) | \([2]\) | \(16896\) | \(0.86197\) | \(\Gamma_0(N)\)-optimal |
| 17457.c2 | 17457a2 | \([1, 1, 0, -6094, -60065]\) | \(169112377/88209\) | \(13058097732801\) | \([2, 2]\) | \(33792\) | \(1.2085\) | |
| 17457.c1 | 17457a3 | \([1, 1, 0, -77509, -8329922]\) | \(347873904937/395307\) | \(58519623172923\) | \([2]\) | \(67584\) | \(1.5551\) | |
| 17457.c4 | 17457a4 | \([1, 1, 0, 23001, -438300]\) | \(9090072503/5845851\) | \(-865395749746539\) | \([2]\) | \(67584\) | \(1.5551\) |
Rank
sage: E.rank()
The elliptic curves in class 17457a have rank \(0\).
Complex multiplication
The elliptic curves in class 17457a do not have complex multiplication.Modular form 17457.2.a.a
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.
