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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 77077l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77077.u4 | 77077l1 | \([1, -1, 0, -93011, -92039480]\) | \(-426957777/17320303\) | \(-3609938775122646967\) | \([2]\) | \(875520\) | \(2.2410\) | \(\Gamma_0(N)\)-optimal |
77077.u3 | 77077l2 | \([1, -1, 0, -3680056, -2701256013]\) | \(26444947540257/169338169\) | \(35293864222893317041\) | \([2, 2]\) | \(1751040\) | \(2.5876\) | |
77077.u2 | 77077l3 | \([1, -1, 0, -5962721, 1051901780]\) | \(112489728522417/62811265517\) | \(13091273455455273091013\) | \([2]\) | \(3502080\) | \(2.9341\) | |
77077.u1 | 77077l4 | \([1, -1, 0, -58790111, -173487316458]\) | \(107818231938348177/4463459\) | \(930284748209667851\) | \([2]\) | \(3502080\) | \(2.9341\) |
Rank
sage: E.rank()
The elliptic curves in class 77077l have rank \(1\).
Complex multiplication
The elliptic curves in class 77077l do not have complex multiplication.Modular form 77077.2.a.l
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 Cremona numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.