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SageMath
E = EllipticCurve("ha1")
E.isogeny_class()
Elliptic curves in class 254800.ha
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 254800.ha1 | 254800ha2 | \([0, -1, 0, -8883128, -10187574928]\) | \(-6434774386429585/140608\) | \(-1693940796620800\) | \([]\) | \(6065280\) | \(2.4485\) | |
| 254800.ha2 | 254800ha1 | \([0, -1, 0, -102328, -15896208]\) | \(-9836106385/3407872\) | \(-41055511851827200\) | \([]\) | \(2021760\) | \(1.8992\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 254800.ha have rank \(0\).
Complex multiplication
The elliptic curves in class 254800.ha do not have complex multiplication.Modular form 254800.2.a.ha
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.
