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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 29624f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29624.d2 | 29624f1 | \([0, 1, 0, 2217392, -186860688]\) | \(7953970437500/4703287687\) | \(-712965502943025912832\) | \([2]\) | \(1013760\) | \(2.6907\) | \(\Gamma_0(N)\)-optimal |
| 29624.d1 | 29624f2 | \([0, 1, 0, -8976248, -1512187664]\) | \(263822189935250/149429406721\) | \(45303634056572538816512\) | \([2]\) | \(2027520\) | \(3.0373\) |
Rank
sage: E.rank()
The elliptic curves in class 29624f have rank \(0\).
Complex multiplication
The elliptic curves in class 29624f do not have complex multiplication.Modular form 29624.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
