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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 99275.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 99275.b1 | 99275c2 | \([1, 0, 0, -279963, -53681708]\) | \(3301293169/218405\) | \(160547744371953125\) | \([2]\) | \(1105920\) | \(2.0509\) | |
| 99275.b2 | 99275c1 | \([1, 0, 0, -54338, 3852667]\) | \(24137569/5225\) | \(3840855128515625\) | \([2]\) | \(552960\) | \(1.7043\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 99275.b have rank \(0\).
Complex multiplication
The elliptic curves in class 99275.b do not have complex multiplication.Modular form 99275.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
