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SageMath
E = EllipticCurve("l1")
E.isogeny_class()
Elliptic curves in class 3465l
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3465.c4 | 3465l1 | \([1, -1, 1, -28418, -118888]\) | \(3481467828171481/2005331497785\) | \(1461886661885265\) | \([2]\) | \(15360\) | \(1.5994\) | \(\Gamma_0(N)\)-optimal |
3465.c2 | 3465l2 | \([1, -1, 1, -323663, -70623394]\) | \(5143681768032498601/14238434358225\) | \(10379818647146025\) | \([2, 2]\) | \(30720\) | \(1.9460\) | |
3465.c1 | 3465l3 | \([1, -1, 1, -5175158, -4530117598]\) | \(21026497979043461623321/161783881875\) | \(117940449886875\) | \([2]\) | \(61440\) | \(2.2926\) | |
3465.c3 | 3465l4 | \([1, -1, 1, -196088, -126960514]\) | \(-1143792273008057401/8897444448004035\) | \(-6486237002594941515\) | \([2]\) | \(61440\) | \(2.2926\) |
Rank
sage: E.rank()
The elliptic curves in class 3465l have rank \(0\).
Complex multiplication
The elliptic curves in class 3465l do not have complex multiplication.Modular form 3465.2.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.