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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 30345.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30345.m1 | 30345bg2 | \([1, 0, 0, -10240, -382333]\) | \(24170156844497/1191196125\) | \(5852346562125\) | \([2]\) | \(55296\) | \(1.2091\) | |
30345.m2 | 30345bg1 | \([1, 0, 0, 385, -23208]\) | \(1284365503/48234375\) | \(-236975484375\) | \([2]\) | \(27648\) | \(0.86249\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30345.m have rank \(1\).
Complex multiplication
The elliptic curves in class 30345.m do not have complex multiplication.Modular form 30345.2.a.m
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.