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SageMath
E = EllipticCurve("gm1")
E.isogeny_class()
Elliptic curves in class 141120.gm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
141120.gm1 | 141120mp2 | \([0, 0, 0, -176988, -27160112]\) | \(1272112/75\) | \(36148567453286400\) | \([2]\) | \(1376256\) | \(1.9304\) | |
141120.gm2 | 141120mp1 | \([0, 0, 0, 8232, -1747928]\) | \(2048/45\) | \(-1355571279498240\) | \([2]\) | \(688128\) | \(1.5839\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 141120.gm have rank \(1\).
Complex multiplication
The elliptic curves in class 141120.gm do not have complex multiplication.Modular form 141120.2.a.gm
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.