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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 12495h
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12495.c4 | 12495h1 | \([1, 1, 1, 685, -11320]\) | \(302111711/669375\) | \(-78751299375\) | \([4]\) | \(12288\) | \(0.77496\) | \(\Gamma_0(N)\)-optimal |
| 12495.c3 | 12495h2 | \([1, 1, 1, -5440, -128920]\) | \(151334226289/28676025\) | \(3373705665225\) | \([2, 2]\) | \(24576\) | \(1.1215\) | |
| 12495.c1 | 12495h3 | \([1, 1, 1, -82615, -9173830]\) | \(530044731605089/26309115\) | \(3095241070635\) | \([2]\) | \(49152\) | \(1.4681\) | |
| 12495.c2 | 12495h4 | \([1, 1, 1, -26265, 1512090]\) | \(17032120495489/1339001685\) | \(157532209238565\) | \([2]\) | \(49152\) | \(1.4681\) |
Rank
sage: E.rank()
The elliptic curves in class 12495h have rank \(0\).
Complex multiplication
The elliptic curves in class 12495h do not have complex multiplication.Modular form 12495.2.a.h
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.
