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SageMath
E = EllipticCurve("he1")
E.isogeny_class()
Elliptic curves in class 244800.he
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244800.he1 | 244800he2 | \([0, 0, 0, -6780, -222640]\) | \(-115431760/4913\) | \(-1467013939200\) | \([]\) | \(207360\) | \(1.1007\) | |
| 244800.he2 | 244800he1 | \([0, 0, 0, 420, -880]\) | \(27440/17\) | \(-5076172800\) | \([]\) | \(69120\) | \(0.55144\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 244800.he have rank \(1\).
Complex multiplication
The elliptic curves in class 244800.he do not have complex multiplication.Modular form 244800.2.a.he
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.
