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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 238260a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 238260.a3 | 238260a1 | \([0, -1, 0, -14921, -912354]\) | \(-488095744/200475\) | \(-150904367895600\) | \([2]\) | \(1026432\) | \(1.4289\) | \(\Gamma_0(N)\)-optimal |
| 238260.a2 | 238260a2 | \([0, -1, 0, -258596, -50524584]\) | \(158792223184/16335\) | \(196734583330560\) | \([2]\) | \(2052864\) | \(1.7755\) | |
| 238260.a4 | 238260a3 | \([0, -1, 0, 115039, 9991290]\) | \(223673040896/187171875\) | \(-140890652124750000\) | \([2]\) | \(3079296\) | \(1.9783\) | |
| 238260.a1 | 238260a4 | \([0, -1, 0, -561836, 88238040]\) | \(1628514404944/664335375\) | \(8001086207063136000\) | \([2]\) | \(6158592\) | \(2.3248\) |
Rank
sage: E.rank()
The elliptic curves in class 238260a have rank \(1\).
Complex multiplication
The elliptic curves in class 238260a do not have complex multiplication.Modular form 238260.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
