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SageMath
E = EllipticCurve("hm1")
E.isogeny_class()
Elliptic curves in class 158400.hm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 158400.hm1 | 158400ei2 | \([0, 0, 0, -3753300, -2798768000]\) | \(125330290485184/378125\) | \(17641800000000000\) | \([2]\) | \(2211840\) | \(2.3451\) | |
| 158400.hm2 | 158400ei1 | \([0, 0, 0, -237675, -42518000]\) | \(2036792051776/107421875\) | \(78310546875000000\) | \([2]\) | \(1105920\) | \(1.9986\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 158400.hm have rank \(1\).
Complex multiplication
The elliptic curves in class 158400.hm do not have complex multiplication.Modular form 158400.2.a.hm
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
