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SageMath
E = EllipticCurve("bl1")
E.isogeny_class()
Elliptic curves in class 11025bl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11025.l2 | 11025bl1 | \([1, -1, 1, -1805, -31678]\) | \(-9317\) | \(-69767578125\) | \([]\) | \(7200\) | \(0.81905\) | \(\Gamma_0(N)\)-optimal |
| 11025.l1 | 11025bl2 | \([1, -1, 1, -46818680, 123315617072]\) | \(-162677523113838677\) | \(-69767578125\) | \([]\) | \(266400\) | \(2.6245\) |
Rank
sage: E.rank()
The elliptic curves in class 11025bl have rank \(0\).
Complex multiplication
The elliptic curves in class 11025bl do not have complex multiplication.Modular form 11025.2.a.bl
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.
\(\left(\begin{array}{rr} 1 & 37 \\ 37 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
