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SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 124950ce
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 124950.m2 | 124950ce1 | \([1, 1, 0, -352825, -80802875]\) | \(105695235625/14688\) | \(675011137500000\) | \([]\) | \(1360800\) | \(1.8626\) | \(\Gamma_0(N)\)-optimal |
| 124950.m1 | 124950ce2 | \([1, 1, 0, -812200, 166984000]\) | \(1289333385625/482967552\) | \(22195566220800000000\) | \([]\) | \(4082400\) | \(2.4119\) |
Rank
sage: E.rank()
The elliptic curves in class 124950ce have rank \(0\).
Complex multiplication
The elliptic curves in class 124950ce do not have complex multiplication.Modular form 124950.2.a.ce
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
