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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 243360.cl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
243360.cl1 | 243360cl4 | \([0, 0, 0, -1910883, -1016565082]\) | \(428320044872/73125\) | \(131741766411840000\) | \([2]\) | \(4128768\) | \(2.2915\) | |
243360.cl2 | 243360cl2 | \([0, 0, 0, -815763, 273979082]\) | \(33324076232/1285245\) | \(2315493286454499840\) | \([2]\) | \(4128768\) | \(2.2915\) | |
243360.cl3 | 243360cl1 | \([0, 0, 0, -131313, -12531688]\) | \(1111934656/342225\) | \(77068933350926400\) | \([2, 2]\) | \(2064384\) | \(1.9450\) | \(\Gamma_0(N)\)-optimal |
243360.cl4 | 243360cl3 | \([0, 0, 0, 363012, -84505408]\) | \(367061696/426465\) | \(-6146543853710807040\) | \([2]\) | \(4128768\) | \(2.2915\) |
Rank
sage: E.rank()
The elliptic curves in class 243360.cl have rank \(0\).
Complex multiplication
The elliptic curves in class 243360.cl do not have complex multiplication.Modular form 243360.2.a.cl
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.