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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 28980.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
28980.e1 | 28980e1 | \([0, 0, 0, -23695293, -44395733783]\) | \(-126142795384287538429696/9315359375\) | \(-108654351750000\) | \([]\) | \(1062720\) | \(2.5895\) | \(\Gamma_0(N)\)-optimal |
28980.e2 | 28980e2 | \([0, 0, 0, -23456793, -45333186383]\) | \(-122372013839654770813696/5297595236711512175\) | \(-61791150841003078009200\) | \([3]\) | \(3188160\) | \(3.1388\) |
Rank
sage: E.rank()
The elliptic curves in class 28980.e have rank \(1\).
Complex multiplication
The elliptic curves in class 28980.e do not have complex multiplication.Modular form 28980.2.a.e
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.