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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 98736.bc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.bc1 | 98736ce2 | \([0, -1, 0, -3931693, -2999447471]\) | \(-14820625871872000/529675443\) | \(-240218203513989888\) | \([]\) | \(1658880\) | \(2.4241\) | |
| 98736.bc2 | 98736ce1 | \([0, -1, 0, -11293, -10220879]\) | \(-351232000/99379467\) | \(-45070537712124672\) | \([]\) | \(552960\) | \(1.8748\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 98736.bc have rank \(0\).
Complex multiplication
The elliptic curves in class 98736.bc do not have complex multiplication.Modular form 98736.2.a.bc
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
