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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 30960.m
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30960.m1 | 30960e4 | \([0, 0, 0, -2229123, 1281000098]\) | \(820480625548035842/5805\) | \(8666818560\) | \([2]\) | \(270336\) | \(1.9613\) | |
30960.m2 | 30960e3 | \([0, 0, 0, -149043, 17061842]\) | \(245245463376482/57692266875\) | \(86134092906240000\) | \([2]\) | \(270336\) | \(1.9613\) | |
30960.m3 | 30960e2 | \([0, 0, 0, -139323, 20014778]\) | \(400649568576484/33698025\) | \(25155440870400\) | \([2, 2]\) | \(135168\) | \(1.6147\) | |
30960.m4 | 30960e1 | \([0, 0, 0, -8103, 358022]\) | \(-315278049616/114259815\) | \(-21323623714560\) | \([2]\) | \(67584\) | \(1.2681\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30960.m have rank \(1\).
Complex multiplication
The elliptic curves in class 30960.m do not have complex multiplication.Modular form 30960.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.