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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 248256.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 248256.a1 | 248256a2 | \([0, 0, 0, -4029852, 3106763930]\) | \(155125609019771539456/401559694321077\) | \(18735169098244168512\) | \([]\) | \(10368000\) | \(2.5739\) | |
| 248256.a2 | 248256a1 | \([0, 0, 0, -229332, -42263350]\) | \(28589738658328576/6184378917\) | \(288538382751552\) | \([]\) | \(2073600\) | \(1.7691\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 248256.a have rank \(0\).
Complex multiplication
The elliptic curves in class 248256.a do not have complex multiplication.Modular form 248256.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
